{"id":172,"date":"2021-06-23T00:55:25","date_gmt":"2021-06-23T00:55:25","guid":{"rendered":"https:\/\/opentextbc.ca\/businesstechnicalmath\/chapter\/decimals\/"},"modified":"2023-11-01T17:52:01","modified_gmt":"2023-11-01T17:52:01","slug":"decimals","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/businesstechnicalmath\/chapter\/decimals\/","title":{"raw":"1.4 Decimals","rendered":"1.4 Decimals"},"content":{"raw":"[latexpage]\r\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Learning Objectives<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nBy the end of this section it is expected that you will be able to:\r\n<ul>\r\n \t<li>Round decimals<\/li>\r\n \t<li>Add and subtract decimals<\/li>\r\n \t<li>Multiply and divide decimals<\/li>\r\n \t<li>Convert decimals, fractions, and percent<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1170655162670\"><strong data-effect=\"bold\">Decimals<\/strong> are another way of writing <span class=\"no-emphasis\" data-type=\"term\">fraction<\/span>s whose denominators are powers of 10.<\/p>\r\n\\(\\begin{array}{cccccccc}\\hfill 0.1&amp; =\\hfill &amp; \\frac{1}{10}\\hfill &amp; &amp; &amp; &amp; &amp; 0.1\\phantom{\\rule{0.2em}{0ex}}\\text{is \u201cone tenth\u201d}\\hfill \\\\ \\hfill 0.01&amp; =\\hfill &amp; \\frac{1}{100}\\hfill &amp; &amp; &amp; &amp; &amp; 0.01\\phantom{\\rule{0.2em}{0ex}}\\text{is \u201cone hundredth\u201d}\\hfill \\\\ \\hfill 0.001&amp; =\\hfill &amp; \\frac{1}{1,000}\\hfill &amp; &amp; &amp; &amp; &amp; \\text{0.001 is \u201cone thousandth\u201d}\\hfill \\\\ \\hfill 0.0001&amp; =\\hfill &amp; \\frac{1}{10,000}\\hfill &amp; &amp; &amp; &amp; &amp; \\text{0.0001 is \u201cone ten-thousandth\u201d}\\hfill \\end{array}\\)\r\n<p id=\"fs-id1170655082460\">Notice that \u201cten thousand\u201d is a number larger than one, but \u201cone ten-thousand<strong data-effect=\"bold\">th<\/strong>\u201d is a number smaller than one. The \u201cth\u201d at the end of the name tells you that the number is smaller than one.<\/p>\r\nWhen we name a whole number, the name corresponds to the place value based on the powers of ten. We read 10,000 as \u201cten thousand\u201d and 10,000,000 as \u201cten million.\u201d Likewise, the names of the <span class=\"no-emphasis\" data-type=\"term\">decimal<\/span> places correspond to their fraction values. <a class=\"autogenerated-content\" href=\"#figure1\">Figure 1<\/a> shows the names of the <span class=\"no-emphasis\" data-type=\"term\">place values<\/span> to the left and right of the decimal point.\r\n<div id=\"CNX_ElemAlg_Figure_01_07_001_new\" class=\"bc-figure figure\">\r\n<div class=\"bc-figcaption figcaption\">Place value of decimal numbers are shown to the left and right of the decimal point.<a id=\"figure1\"><\/a><\/div>\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"286\"]<a href=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_001_new.jpg\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_001_new.jpg\" alt=\"A table is shown with the title Place Value. From left to right the row reads \u201cHundred thousands,\u201d \u201cTen thousands,\u201d \u201cThousands,\u201d \u201cHundreds,\u201d \u201cTens,\u201d and \u201cOnes.\u201d Then there is a blank cell and below it is a decimal point. To the right of this, the cells read \u201cTenths,\u201d \u201cHundredths,\u201d \u201cThousandths,\u201d \u201cTen-thousandths,\u201d and \u201cHundred-thousandths.\u201d\" width=\"286\" height=\"260\" data-media-type=\"image\/jpeg\" \/><\/a> Figure 1[\/caption]\r\n\r\n<\/div>\r\n<h1>Round Decimals<\/h1>\r\n<p id=\"fs-id1170654977720\">Rounding decimals is very much like rounding whole numbers. We will round decimals with a method based on the one we used to round whole numbers.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div data-type=\"title\">Round 18.379 to the nearest hundredth.<\/div>\r\n<div id=\"fs-id1170654965636\" data-type=\"exercise\">\r\n<div id=\"fs-id1170655213305\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<span id=\"fs-id1170655218662\" data-type=\"media\" data-alt=\"A table is given with four steps. The first step reads \u201cStep 1: Locate the given place value and mark it with an arrow.\u201d To the right of this, we have the number 18.379; above it, are the words hundreds place, which has an arrow pointing to the 7.\"><img title=\"A table is given with four steps. The first step reads \u201cStep 1: Locate the given place value and mark it with an arrow.\u201d To the right of this, we have the number 18.379; above it, are the words hundreds place, which has an arrow pointing to the 7.\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_004a_new.jpg\" alt=\"A table is given with four steps. The first step reads \u201cStep 1: Locate the given place value and mark it with an arrow.\u201d To the right of this, we have the number 18.379; above it, are the words hundreds place, which has an arrow pointing to the 7.\" data-media-type=\"image\/jpeg\" data-popupalt-original-title=\"null\" \/><\/span><span id=\"fs-id1170653985218\" data-type=\"media\" data-alt=\"The second step reads \u201cStep 2. Underline the digit to the right of the given place value.\u201d To the right of this, we have 18.379 with the 9 underlined.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_004b_new.jpg\" alt=\"The second step reads \u201cStep 2. Underline the digit to the right of the given place value.\u201d To the right of this, we have 18.379 with the 9 underlined.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170653901496\" data-type=\"media\" data-alt=\"The third step reads \u201cStep 3. Is this digit greater than or equal to 5? Below this reads, \u201cYes: add 1 to the digit in the given place value.\u201d Below this reads, \u201cNo: do not change the digit in the given place value.\u201d To the right of this, it says \u201cBecause 9 is greater than or equal to \u201d To the right of this, we have the number 18.379 with the 9 marked \u201cdelete\u201d and the 7 marked \u201cadd 1.\u201d\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_004c_new.jpg\" alt=\"The third step reads \u201cStep 3. Is this digit greater than or equal to 5? Below this reads, \u201cYes: add 1 to the digit in the given place value.\u201d Below this reads, \u201cNo: do not change the digit in the given place value.\u201d To the right of this, it says \u201cBecause 9 is greater than or equal to \u201d To the right of this, we have the number 18.379 with the 9 marked \u201cdelete\u201d and the 7 marked \u201cadd 1.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170653744228\" data-type=\"media\" data-alt=\"Finally, the last step reads \u201cStep 4. Rewrite the number, removing all digits to the right of the rounding digit.\u201d To the right of this, we have 18.38 followed by \u201c18.38 is 18.379 rounded to the nearest hundredth.\u201d\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_004d_new.jpg\" alt=\"Finally, the last step reads \u201cStep 4. Rewrite the number, removing all digits to the right of the rounding digit.\u201d To the right of this, we have 18.38 followed by \u201c18.38 is 18.379 rounded to the nearest hundredth.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div data-type=\"problem\">\r\n<p id=\"fs-id1170654954676\">Round to the nearest hundredth: \\(1.047\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655195781\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170654903945\">1.05<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1170655029280\">We summarize the steps for rounding a <span class=\"no-emphasis\" data-type=\"term\">decimal<\/span> here.<\/p>\r\n\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">HOW TO: Round Decimals<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<ol id=\"fs-id1166424888811\" class=\"stepwise\" type=\"1\">\r\n \t<li>Locate the given place value and mark it with an arrow.<\/li>\r\n \t<li>Underline the digit to the right of the place value.<\/li>\r\n \t<li>Is this digit greater than or equal to 5?\r\n<ul data-bullet-style=\"bullet\">\r\n \t<li>Yes\u2014add 1 to the digit in the given place value.<\/li>\r\n \t<li>No\u2014do <u data-effect=\"underline\">not<\/u> change the digit in the given place value.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Rewrite the number, deleting all digits to the right of the rounding digit.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1170653237730\" class=\"howto\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nRound 18.379 to the nearest a) tenth b) whole number.\r\n<div id=\"fs-id1170654872675\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id1170654935270\">Round 18.379<\/p>\r\na) to the nearest tenth\r\n<table id=\"eip-id1169752878832\" style=\"width: 100%;\" summary=\"A table is given with four steps. The first step reads \u201cLocate the tenths place and mark it with an arrow.\u201d To the right of this, we have the number 18.379; below it is written tenths place, which has an arrow pointing to the 3. The second step reads \u201cUnderline the digit to the right of the tenths digit.\u201d To the right of this, we have 18.379 with the 7 underlined. The third step reads \u201cBecause 7 is greater than or equal to 5, add 1 to the 3.\u201d To the right of this, we have the number 18.379 with the 7 and 9 marked \u201cdelete\u201d and the 3 marked \u201cadd 1.\u201d Finally, the last step reads \u201cRewrite the number, deleting all digits to the right of the tenths place.\u201d To the right of this, we have 18.4 followed by \u201cSo, 18.379 rounded to the nearest tenth is 18.4.\u201d\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>Locate the tenths place with an arrow.<\/td>\r\n<td><span id=\"eip-id1169752964044\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_005a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Underline the digit to the right of the given place value.<\/td>\r\n<td><span id=\"eip-id1169752799574\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_005b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Because 7 is greater than or equal to 5, add 1 to the 3.<\/td>\r\n<td><span id=\"eip-id1169750840488\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_005c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite the number, deleting all digits to the right of the rounding digit.<\/td>\r\n<td><span id=\"eip-id1169750591270\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_005d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Notice that the deleted digits were NOT replaced with zeros.<\/td>\r\n<td>So, 18.379 rounded to the nearest tenth is 18.4.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n\r\nb) to the nearest whole number\r\n<table id=\"eip-id1169754002832\" style=\"width: 100%;\" summary=\"A table is given with four steps. The first step reads \u201cLocate the ones place and mark it with an arrow.\u201d To the right of this, we have the number 18.379; below it is written ones place, which has an arrow pointing to the 8. The second step reads \u201cUnderline the digit to the right of the ones place.\u201d To the right of this, we have 18.379 with the 3 underlined. The third step reads \u201cSince 3 is not greater than or equal to 5, do not add 1 to the 8.\u201d To the right of this, we have the number 18.379 with the 3, 7, and 9 marked \u201cdelete\u201d and the 8 marked \u201cdo not add 1.\u201d Finally, the last step reads \u201cRewrite the number, deleting all digits to the right of the ones place.\u201d To the right of this, we have 18 followed by \u201cSo 18.379 rounded to the nearest whole number is 18.\u201d\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>Locate the ones place with an arrow.<\/td>\r\n<td><span id=\"eip-id1169754058794\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_006a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Underline the digit to the right of the given place value.<\/td>\r\n<td><span id=\"eip-id1169754058811\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_006b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Since 3 is not greater than or equal to 5, do not add 1 to the 8.<\/td>\r\n<td><span id=\"eip-id1169754362233\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_006c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite the number, deleting all digits to the right of the rounding digit.<\/td>\r\n<td><span id=\"eip-id1169754362250\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_006d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>So, 18.379 rounded to the nearest whole number is 18.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655025740\" data-type=\"problem\">\r\n\r\nRound \\(6.582\\) to the nearest a) hundredth b) tenth c) whole number.\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655105998\" data-type=\"solution\"><details><summary>Show answer<\/summary>a) 6.58 b) 6.6 c) 7\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<h1>Add and Subtract Decimals<\/h1>\r\n<p id=\"fs-id1170655154216\">To add or subtract decimals, we line up the decimal points. By lining up the decimal points this way, we can add or subtract the corresponding <span class=\"no-emphasis\" data-type=\"term\">place values<\/span>. We then add or subtract the numbers as if they were whole numbers and then place the decimal point in the sum.<\/p>\r\n\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">HOW TO: Add or Subtract Decimals<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<ol id=\"fs-id1166422560823\" class=\"stepwise\" type=\"1\">\r\n \t<li>Write the numbers so the decimal points line up vertically.<\/li>\r\n \t<li>Use zeros as place holders, as needed.<\/li>\r\n \t<li>Add or subtract the numbers as if they were whole numbers. Then place the decimal point in the answer under the decimal points in the given numbers.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div class=\"howto\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div data-type=\"problem\">\r\n<p id=\"fs-id1170654982792\">Add: \\(23.5+41.38\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654944111\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<table id=\"eip-474\" style=\"height: 90px;\" summary=\".\">\r\n<tbody>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 487.406px;\">Write the numbers so the decimal points line up vertically.<\/td>\r\n<td style=\"height: 14px; width: 761.406px;\">\\(\\underline{\\begin{array}{c}\\phantom{\\rule{0.7em}{0ex}}23.5\\hfill \\\\ +41.38\\hfill \\end{array}}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 46px;\">\r\n<td style=\"height: 46px; width: 487.406px;\">Put 0 as a placeholder after the 5 in 23.5.\r\nRemember, \\(\\frac{5}{10}=\\frac{50}{100}\\phantom{\\rule{0.5em}{0ex}}\\text{so}\\phantom{\\rule{0.5em}{0ex}}0.5=0.50\\).<\/td>\r\n<td style=\"height: 46px; width: 761.406px;\">\\(\\begin{array}{c}\\underline{\\begin{array}{c}\\phantom{\\rule{0.7em}{0ex}}23.50\\hfill \\\\ +41.38\\hfill \\end{array}}\\end{array}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 30px;\">\r\n<td style=\"height: 30px; width: 487.406px;\">Add the numbers as if they were whole numbers.\r\nThen place the decimal point in the sum.<\/td>\r\n<td style=\"height: 30px; width: 761.406px;\">\\(\\begin{array}{c}\\underline{\\begin{array}{c}\\phantom{\\rule{0.7em}{0ex}}23.50\\hfill \\\\ +41.38\\hfill \\end{array}}\\hfill \\\\ \\phantom{\\rule{0.7em}{0ex}}64.88\\hfill \\end{array}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 3<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655114138\" data-type=\"problem\">\r\n<p id=\"fs-id1170655213420\">Add: \\(4.8+11.69\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654919229\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170655167053\">16.49<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1170653235826\" class=\"try\" data-type=\"note\">\r\n<div data-type=\"exercise\">\r\n<div id=\"fs-id1170655208527\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654921340\" data-type=\"problem\">\r\n<p id=\"fs-id1170655162342\">Subtract: \\(20-14.65\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655067989\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<table id=\"eip-645\" style=\"width: 100%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>\\(20-14.65\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the numbers so the decimal points line up vertically.\r\nRemember, 20 is a whole number, so place the decimal point after the 0.<\/td>\r\n<td>\\(\\underline{\\begin{array}{c}\\phantom{\\rule{0.7em}{0ex}}20.\\hfill \\\\ -14.65\\end{array}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Put in zeros to the right as placeholders.<\/td>\r\n<td>\\(\\begin{array}{c}\\phantom{\\rule{0.7em}{0ex}}20.00\\hfill \\\\ \\underline{-14.65}\\hfill \\end{array}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract and place the decimal point in the answer.<\/td>\r\n<td>\\(\\begin{array}{c}\\underline{\\begin{array}{c}\\phantom{\\rule{0.8em}{0ex}}\\stackrel{1}{\\overline{)2}}\\stackrel{\\stackrel{9}{\\overline{)10}}}{\\overline{)0}}.\\stackrel{\\stackrel{9}{\\overline{)10}}}{\\overline{)0}}\\stackrel{\\overline{)10}}{\\overline{)0}}\\hfill \\\\ -\\phantom{\\rule{0.2em}{0ex}}1\\phantom{\\rule{0.2em}{0ex}}4\\phantom{\\rule{0.4em}{0ex}}.\\phantom{\\rule{0.2em}{0ex}}6\\phantom{\\rule{0.4em}{0ex}}5\\hfill \\end{array}}\\hfill \\\\ \\phantom{\\rule{1.8em}{0ex}}5\\phantom{\\rule{0.4em}{0ex}}.\\phantom{\\rule{0.2em}{0ex}}3\\phantom{\\rule{0.4em}{0ex}}5\\hfill \\end{array}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 4<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654965912\" data-type=\"problem\">\r\n<p id=\"fs-id1170655215425\">Subtract: \\(10-9.58\\).<\/p>\r\n\r\n<\/div>\r\n<div data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170655226477\">0.42<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<h1>Multiply and Divide Decimals<\/h1>\r\n<p id=\"fs-id1170655129811\">Multiplying decimals is very much like multiplying whole numbers\u2014we just have to determine where to place the decimal point. The procedure for multiplying decimals will make sense if we first convert them to fractions and then multiply.<\/p>\r\n<p id=\"fs-id1170655215976\">So let\u2019s see what we would get as the <span class=\"no-emphasis\" data-type=\"term\">product<\/span> of decimals by converting them to fractions first. We will do two examples side-by-side. Look for a pattern!<\/p>\r\n\r\n<table id=\"eip-id1169754130025\" style=\"width: 100%;\" summary=\"The numbers 0.3, 0.7, 0.2, and 0.46 are shown, with the first three all marked \u201c1 place\u201d and 0.46 marked \u201c2 places.\u201d Below this line, the instruction \u201cConvert to fractions\u201d is given. We have 3\/10 times 7\/10 and 2\/10 times 46\/100. Note that these fractions correspond to the numbers given above. Then the instruction is given to multiply the numbers, so we have 21\/100 and 92\/1000. The next line instructs us to \u201cConvert to decimals.\u201d We are left with 0.21, which is marked as having \u201c2 places,\u201d and 0.092, which is marked as having \u201c3 places.\u201d\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"eip-id1169754130042\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_009a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">Convert to fractions.\\(\\phantom{\\rule{8em}{0ex}}\\)<\/td>\r\n<td><span id=\"eip-id1169753944283\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_009b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td><span id=\"eip-id1169753944299\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_009c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Convert to decimals.<\/td>\r\n<td><span id=\"eip-id1169753944316\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_009d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1170655162411\">Notice, in the first example, we multiplied two numbers that each had one digit after the decimal point and the product had two decimal places. In the second example, we multiplied a number with one decimal place by a number with two decimal places and the product had three decimal places.<\/p>\r\n<p id=\"fs-id1170655062737\">We multiply the numbers just as we do whole numbers, temporarily ignoring the decimal point. We then count the number of decimal points in the factors and that sum tells us the number of decimal places in the product.<\/p>\r\n<p id=\"fs-id1170655029564\">The rules for multiplying positive and negative numbers apply to decimals, too, of course!<\/p>\r\n<p id=\"fs-id1170655121723\">When <em data-effect=\"italics\">multiplying<\/em> two numbers,<\/p>\r\n\r\n<ul id=\"fs-id1170655188642\" data-bullet-style=\"bullet\">\r\n \t<li>if their signs are the <em data-effect=\"italics\">same<\/em> the product is <em data-effect=\"italics\">positive<\/em>.<\/li>\r\n \t<li>if their signs are <em data-effect=\"italics\">different<\/em> the product is <em data-effect=\"italics\">negative<\/em>.<\/li>\r\n<\/ul>\r\n<p id=\"fs-id1170655028705\">When we multiply signed decimals, first we determine the sign of the product and then multiply as if the numbers were both positive. Finally, we write the product with the appropriate sign.<\/p>\r\n\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">HOW TO: Multiply Decimals<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<ol id=\"fs-id1166424905197\" class=\"stepwise\" type=\"1\">\r\n \t<li>Determine the sign of the product.<\/li>\r\n \t<li>Write in vertical format, lining up the numbers on the right. Multiply the numbers as if they were whole numbers, temporarily ignoring the decimal points.<\/li>\r\n \t<li>Place the decimal point. The number of decimal places in the product is the sum of the number of decimal places in the factors.<\/li>\r\n \t<li>Write the product with the appropriate sign.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1170654988259\" class=\"howto\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655075135\" data-type=\"problem\">\r\n<p id=\"fs-id1170655208074\">Multiply: \\(\\left(-3.9\\right)\\left(4.075\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655111654\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1169753348487\" style=\"width: 100%;\" summary=\"The expression 3.9 times 4.075 is given. A table is given with descriptions of steps on the left and the mathematical work on the right. The first step reads \u201cDetermine the sign of the product. The signs are the same.\u201d To the right of this, we have \u201cThe product will be positive.\u201d The second step reads \u201cWrite the numbers in vertical format, lining up the numbers on the right.\u201d To the right of this, we have 4.075 on one line, and below it we have the times symbol followed by 3.9. The numbers are aligned on their right, so 5 is above 9. Then, there is a solid horizontal line below our numbers. Then the third step reads \u201cMultiply the numbers as if they were whole numbers, temporarily ignoring the decimal points.\u201d We again have 4.075 on one line, and below it we have the times symbol followed by 3.9. The numbers are again aligned on their right, so 5 is above 9, there is a solid horizontal line below our numbers. Now, there are other numbers underneath this line: specifically, the number 36675 and below that there is the number 12225, which is shifted over one space so that the 7 from 36675 lines up with the 5 from 12225. Below these numbers there is another solid horizontal line, below which there is the number 158925. Then the fourth step reads \u201cPlace the decimal points. Add the number of decimal places in the factors (1 plus 3). Place the decimal point 4 places from the right.\u201d To the right of this, we have the same setup as in the previous line, however, the number 4.075 is marked \u201c3 places,\u201d the number 3.9 is marked \u201c1 place,\u201d and the number 158925 is marked \u201c4 places.\u201d\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>(\u22123.9)(4.075)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The signs are different. The product will be negative.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write in vertical format, lining up the numbers on the right.<\/td>\r\n<td><span id=\"eip-id1169752872718\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_010b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td><span id=\"eip-id1169750874908\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_010c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the number of decimal places in the factors (1 + 3).\r\n\r\n<span id=\"eip-id1169753269067\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_010a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span>\r\nPlace the decimal point 4 places from the right.<\/td>\r\n<td><span id=\"eip-id1169753284625\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_010d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The signs are different, so the product is negative.<\/td>\r\n<td>(\u22123.9)(4.075) = \u221215.8925<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 5<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655057717\" data-type=\"problem\">\r\n<p id=\"fs-id1170655083436\">Multiply: \\(-4.5\\left(6.107\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655025662\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170655037473\">\\(-27.4815\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1170655107014\">In many of your other classes, especially in the sciences, you will multiply decimals by powers of 10 (10, 100, 1000, etc.). If you multiply a few products on paper, you may notice a pattern relating the number of zeros in the power of 10 to number of decimal places we move the decimal point to the right to get the product.<\/p>\r\n\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">HOW TO: Multiply a Decimal by a Power of Ten<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<ol id=\"fs-id1166422556911\" class=\"stepwise\" type=\"1\">\r\n \t<li>Move the decimal point to the right the same number of places as the number of zeros in the power of 10.<\/li>\r\n \t<li>Add zeros at the end of the number as needed.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1170654972139\" class=\"howto\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654981723\" data-type=\"problem\">\r\n<p id=\"fs-id1170655088072\">Multiply 5.63 a) by 10 b) by 100 c) by 1,000.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655174581\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id1170654915804\">By looking at the number of zeros in the multiple of ten, we see the number of places we need to move the decimal to the right.<\/p>\r\n<p id=\"fs-id1166424779193\">a)<\/p>\r\n\r\n<table id=\"eip-id1169752865183\" style=\"width: 100%;\" summary=\"The expression 5.63 times 10 is given. The directions read \u201cThere is 1 zero in 10, so move the decimal point 1 place to the right.\u201d The number 5.63 is shown with an arrow starting from the decimal point and moving to the space between 6 and 3. Then the number 56.3 is given.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>5.63(10)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>There is 1 zero in 10, so move the decimal point 1 place to the right.<\/td>\r\n<td><span id=\"eip-id1169753258712\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_011_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nb)\r\n<table id=\"eip-id1169752935718\" style=\"width: 100%;\" summary=\"The expression 5.63 times 100 is given. The directions read \u201cThere are 2 zeros in 100, so move the decimal point 2 places to the right.\u201d The number 5.63 is shown with an arrow starting from the decimal point, moving to the space between 6 and 3, and then moving further to the space after 3. Then the number 563 is given.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>5.63(100)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>There are 2 zeros in 100, so move the decimal point 2 places to the right.<\/td>\r\n<td><span id=\"eip-id1169752908904\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_012_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nc)\r\n<table id=\"eip-id1169751883861\" style=\"width: 100%;\" summary=\"The expression 5.63 times 1,000 is given. The directions read \u201cThere are 3 zeros in 1,000, so move the decimal point 3 places to the right.\u201d The number 5.63 is shown with an arrow starting from the decimal point, moving to the space between 6 and 3, moving further to the space after 3, and then moving one space over from that space. The directions read \u201cA zero must be added at the end.\u201d Then the number 5,630 is given.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>5.63(1,000)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>There are 3 zeros in 1,000, so move the decimal point 3 places to the right.<\/td>\r\n<td><span id=\"eip-id1169749465627\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_013a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>A zero must be added at the end.<\/td>\r\n<td><span id=\"eip-id1169754029608\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_013b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 6<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655150426\" data-type=\"problem\">\r\n<p id=\"fs-id1170655089696\">Multiply 2.58 a) by 10 b) by 100 c) by 1,000.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654981785\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170655196937\">a) 25.8 b) 258 c) 2,580<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\nJust as with multiplication, division of decimals is very much like dividing whole numbers. We just have to figure out where the decimal point must be placed.\r\n\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1170654953534\">To divide decimals, determine what power of 10 to multiply the denominator by to make it a whole number. Then multiply the numerator by that same power of \\(10\\). Because of the equivalent fractions property, we haven\u2019t changed the value of the fraction! The effect is to move the decimal points in the numerator and denominator the same number of places to the right. For example:<\/p>\r\n\\(\\begin{array}{c}\\hfill \\frac{0.8}{0.4}\\hfill \\\\ \\hfill \\frac{0.8\\left(10\\right)}{0.4\\left(10\\right)}\\hfill \\\\ \\hfill \\frac{8}{4}\\hfill \\end{array}\\)\r\n<p id=\"fs-id1170654941815\">We use the rules for dividing positive and negative numbers with decimals, too. When dividing signed decimals, first determine the sign of the quotient and then divide as if the numbers were both positive. Finally, write the quotient with the appropriate sign.<\/p>\r\n<p id=\"fs-id1170655133056\">We review the notation and vocabulary for division:<\/p>\r\n\\(\\underset{\\text{dividend}}{a}\\div \\underset{\\text{divisor}}{b}=\\underset{\\text{quotient}}{\\text{c}}\\phantom{\\rule{5em}{0ex}}\\underset{\\text{divisor}}{b}\\begin{array}{c}\\hfill \\underset{\\text{quotient}}{\\text{c}}\\\\ \\hfill \\overline{)\\underset{\\text{dividend}}{a}}\\end{array}\\)\r\n<p id=\"fs-id1170654928702\">We\u2019ll write the steps to take when dividing decimals, for easy reference.<\/p>\r\n\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">HOW TO: Divide Decimals<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<ol id=\"fs-id1166422823773\" class=\"stepwise\" type=\"1\">\r\n \t<li>Determine the sign of the quotient.<\/li>\r\n \t<li>Make the divisor a whole number by \u201cmoving\u201d the decimal point all the way to the right. \u201cMove\u201d the decimal point in the dividend the same number of places\u2014adding zeros as needed.<\/li>\r\n \t<li>Divide. Place the decimal point in the quotient above the decimal point in the dividend.<\/li>\r\n \t<li>Write the quotient with the appropriate sign.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1170655089296\" class=\"howto\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654962371\" data-type=\"problem\">\r\n<p id=\"fs-id1170654935439\">Divide: \\(-25.56\\div\\left(-0.06\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654969632\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id1170655041701\">Remember, you can \u201cmove\u201d the decimals in the divisor and dividend because of the Equivalent Fractions Property.<\/p>\r\n\r\n<table id=\"eip-id1169754369321\" style=\"height: 288px; width: 100%;\" summary=\"The expression negative 25.65 divided by negative 0.06 is given. A table is given with directions on the left and the mathematical steps on the right. The first step reads \u201cThe signs are the same.\u201d To the right of this, we have \u201cThe quotient is positive.\u201d The second and third steps, respectively, read \u201cMake the divisor a whole number by &#96;moving\u2019 the decimal point all the way to the right\u201d and \u201cMove the decimal point in the dividend the same number of places.\u201d To the right of this, we have a long division problem set up with 0.06 dividing 25.65, but for both 0.06 and 25.65 there are arrows from the decimal points to the space after the last number. The fourth step reads \u201cDivide. Place the decimal point in the quotient above the decimal point in the dividend.\u201d To the right of this, we have a long division problem set up with 006. Dividing 2565.0. The quotient is given as 427.5. To show the work, below 2565.0, it reads negative 24, solid horizontal line, 16, negative 12, solid horizontal line, 45, negative 42, solid horizontal line, 30, 30, and a final solid horizontal line. The fifth step reads \u201cWrite the quotient with the appropriate sign.\u201d To the right of this, we have negative 25.65 divided by negative 0.06 equals 427.5.\" data-label=\"\">\r\n<tbody>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"height: 16px; width: 413.203px;\"><\/td>\r\n<td style=\"height: 16px; width: 221.016px;\">\\(-25.65\\div\\left(-0.06\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"height: 16px; width: 413.203px;\">The signs are the same.<\/td>\r\n<td style=\"height: 16px; width: 221.016px;\">The quotient is positive.<\/td>\r\n<\/tr>\r\n<tr style=\"height: 32px;\">\r\n<td style=\"height: 32px; width: 413.203px;\">Make the divisor a whole number by \u201cmoving\u201d the decimal point all the way to the right.<\/td>\r\n<td style=\"height: 32px; width: 221.016px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 32px;\">\r\n<td style=\"height: 32px; width: 413.203px;\">\u201cMove\u201d the decimal point in the dividend the same number of places.<\/td>\r\n<td style=\"height: 32px; width: 221.016px;\"><span id=\"eip-id1169751952546\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_014a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 160px;\">\r\n<td style=\"height: 160px; width: 413.203px;\">Divide.\r\nPlace the decimal point in the quotient above the decimal point in the dividend.<\/td>\r\n<td style=\"height: 160px; width: 221.016px;\"><span id=\"eip-id1169751952565\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_014b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 32px;\">\r\n<td style=\"height: 32px; width: 413.203px;\">Write the quotient with the appropriate sign.<\/td>\r\n<td style=\"height: 32px; width: 221.016px;\">\\(-25.65\\div\\left(-0.06\\right)=427.5\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 7<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655353521\" data-type=\"problem\">\r\n<p id=\"fs-id1170655230047\">Divide: \\(-23.492\\div\\left(-0.04\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654931861\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170655351826\">587.3<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1170655124340\">A common application of dividing whole numbers into decimals is when we want to find the price of one item that is sold as part of a multi-pack. For example, suppose a case of 24 water bottles costs \\$3.99. To find the price of one water bottle, we would divide \\$3.99 by 24. We show this division in the next example. In calculations with money, we will round the answer to the nearest cent (hundredth).<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654938076\" data-type=\"problem\">\r\n<p id=\"fs-id1170654981962\">Divide: \\(\\$3.99\\div24\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655133913\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1169754137615\" class=\"unnumbered unstyled can-break\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>\\(\\$3.99\\div24\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Place the decimal point in the quotient above the decimal point in the dividend.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide as usual.\r\nWhen do we stop? Since this division involves money, we round it to the nearest cent (hundredth.) To do this, we must carry the division to the thousandths place.<\/td>\r\n<td><span id=\"eip-id1169754122161\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_015_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Round to the nearest cent.<\/td>\r\n<td>\\(\\$0.166\\approx \\$0.17\\)\r\n\\(\\$3.99\\div 24\\approx \\$0.17\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 8<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655104719\" data-type=\"problem\">\r\n<p id=\"fs-id1170654943489\">Divide: \\(\\$6.99\\div 36\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654983050\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170655354181\">\\$0.19<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<h1>Convert Decimals and Fractions<\/h1>\r\n<p id=\"fs-id1170654915544\">We convert decimals into fractions by identifying the place value of the last (farthest right) digit. In the decimal 0.03 the 3 is in the hundredths place, so 100 is the denominator of the fraction equivalent to 0.03<\/p>\r\n\\(0\\phantom{\\rule{0.2em}{0ex}}0.03=\\frac{3}{100}\\)\r\n<p id=\"fs-id1170655205009\">Notice, when the number to the left of the decimal is zero, we get a fraction whose numerator is less than its denominator. Fractions like this are called <span class=\"no-emphasis\" data-type=\"term\">proper fractions<\/span>.<\/p>\r\n<p id=\"fs-id1170655197111\">The steps to take to convert a decimal to a fraction are summarized in the procedure box.<\/p>\r\n\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">HOW TO: Covert a Decimal to a Proper Fraction<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<ol id=\"fs-id1166422823849\" class=\"stepwise\" type=\"1\">\r\n \t<li>Determine the place value of the final digit.<\/li>\r\n \t<li>Write the fraction.\r\n<ul id=\"fs-id1170655121293\" data-bullet-style=\"bullet\">\r\n \t<li>numerator\u2014the \u201cnumbers\u201d to the right of the decimal point<\/li>\r\n \t<li>denominator\u2014the place value corresponding to the final digit<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1170655206712\" class=\"howto\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655150644\" data-type=\"problem\">\r\n<p id=\"fs-id1170654986180\">Write 0.374 as a fraction.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655205678\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<table id=\"eip-id1169752838117\" style=\"width: 100%;\" summary=\"The number 0.374 is given. A table is given with directions on the left and the mathematical steps on the right. The first step reads \u201cDetermine the place value of the final digit.\u201d To the right of this, we have 0.3 marked as tenths, 7 marked as hundredths, and 4 marked as thousandths. The second step reads \u201cWrite the fraction: The numerator is 374.\u201d To the right of this, we have 374\/1,000. The third step reads \u201cSimplify the fraction.\u201d To the right of this, we have the quantity (2 times 187) divided by the quantity (2 times 500). The fourth step reads \u201cDivide out the common factors.\u201d To the right of this, we have 187\/500. So 0.374 equals 187 over 500.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td data-align=\"center\">\\(0.374\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Determine the place value of the final digit.<\/td>\r\n<td data-align=\"center\"><span id=\"eip-id1169752926445\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_016_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the fraction for 0.374:\r\n<ul id=\"eip-id1169752926531\" data-bullet-style=\"\">\r\n \t<li>The numerator is 374.<\/li>\r\n \t<li>The denominator is 1,000.<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td data-align=\"center\">\\(\\frac{374}{1000}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the fraction.<\/td>\r\n<td data-align=\"center\">\\(\\frac{2\\cdot 187}{2\\cdot 500}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide out the common factors.<\/td>\r\n<td data-align=\"center\">\\(\\frac{187}{500}\\)\r\nso, \\(0.374=\\frac{187}{500}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1170654965315\">Did you notice that the number of zeros in the denominator of \\(\\frac{374}{1,000}\\) is the same as the number of decimal places in 0.374?<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 9<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655351640\" data-type=\"problem\">\r\n\r\nWrite 0.234 as a fraction.\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655158112\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170655125808\">\\(\\frac{117}{500}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\nWe\u2019ve learned to convert decimals to fractions. Now we will do the reverse\u2014convert fractions to decimals. Remember that the fraction bar means division. So \\(\\frac{4}{5}\\) can be written \\(4\\div5\\) or \\(5\\overline{)4}\\). This leads to the following method for converting a fraction to a decimal.\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">HOW TO: Covert a Fraction to a Decimal<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nTo convert a fraction to a decimal, divide the numerator of the fraction by the denominator of the fraction.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1170655222662\" class=\"howto\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655150719\" data-type=\"problem\">\r\n<p id=\"fs-id1170655105604\">Write \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{5}{8}\\) as a decimal.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655124919\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id1170655124777\">Since a fraction bar means division, we begin by writing \\(\\frac{5}{8}\\) as \\(8\\overline{)5}\\). Now divide.<\/p>\r\n<span id=\"fs-id1170654966693\" data-type=\"media\" data-alt=\"This is a long division problem with 8 dividing 5.000 and 0.625 as the quotient. Below 5.000 we have 48, a solid horizontal line, 20, 16, a solid horizontal line, 40, 40, and a final horizontal line. So five eighths equals 0.625.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_017_img_new.jpg\" alt=\"This is a long division problem with 8 dividing 5.000 and 0.625 as the quotient. Below 5.000 we have 48, a solid horizontal line, 20, 16, a solid horizontal line, 40, 40, and a final horizontal line. So five eighths equals 0.625.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 10<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655024912\" data-type=\"problem\">\r\n<p id=\"fs-id1170655229974\">Write \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{7}{8}\\) as a decimal.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655154221\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170655129731\">\\(-0.875\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\nWhen we divide, we will not always get a zero remainder. Sometimes the quotient ends up with a decimal that repeats. A repeating decimal is a decimal in which the last digit or group of digits repeats endlessly. A bar is placed over the repeating block of digits to indicate it repeats.\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1170655219747\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Repeating Decimal<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nA <strong data-effect=\"bold\">repeating decimal<\/strong> is a decimal in which the last digit or group of digits repeats endlessly.\r\n\r\n<\/div>\r\n<\/div>\r\nA bar is placed over the repeating block of digits to indicate it repeats.\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654919361\" data-type=\"problem\">\r\n<p id=\"fs-id1170654924199\">Write \\(\\frac{43}{22}\\) as a decimal.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655025946\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<\/div>\r\n<div data-type=\"title\"><\/div>\r\n<div id=\"fs-id1170655025946\" data-type=\"solution\">\r\n\r\n<span id=\"fs-id1170654982890\" data-type=\"media\" data-alt=\"The number 43\/22 is given. The direction is given to \u201cDivide 43 by 22.\u201d A long division problem is given with 22 dividing 43.00000 with 1.95454 as the quotient. Below 43.00000 we have 22, a solid horizontal line, 210, 198, a solid horizontal line, 120, 110, a horizontal line, 100, 88, a solid horizontal line, 120, 110, a solid horizontal line, 100, 88, a solid horizontal line, and then three dots. It is noted that the 120 repeats and that the 100 repeats. This is further explicated as \u201cThe pattern repeats, so the numbers in the quotient will repeat as well. At the end, we are given the statement that 43\/22 equals 1.954 with a small horizontal line over the 54.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_018_img_new.jpg\" alt=\"The number 43\/22 is given. The direction is given to \u201cDivide 43 by 22.\u201d A long division problem is given with 22 dividing 43.00000 with 1.95454 as the quotient. Below 43.00000 we have 22, a solid horizontal line, 210, 198, a solid horizontal line, 120, 110, a horizontal line, 100, 88, a solid horizontal line, 120, 110, a solid horizontal line, 100, 88, a solid horizontal line, and then three dots. It is noted that the 120 repeats and that the 100 repeats. This is further explicated as \u201cThe pattern repeats, so the numbers in the quotient will repeat as well. At the end, we are given the statement that 43\/22 equals 1.954 with a small horizontal line over the 54.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 11<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655154772\" data-type=\"problem\">\r\n<p id=\"fs-id1170655125921\">Write \\(\\frac{27}{11}\\) as a decimal.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655163739\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170655166549\">\\(2.\\stackrel{\\text{\u2014}}{45}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1170654958830\">Sometimes we may have to simplify expressions with fractions and decimals together.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655154796\" data-type=\"problem\">\r\n<p id=\"fs-id1170655089358\">Simplify: \\(\\frac{7}{8}+6.4\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654929183\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id1170655026448\">First we must change one number so both numbers are in the same form. We can change the fraction to a decimal, or change the decimal to a fraction. Usually it is easier to change the fraction to a decimal.<\/p>\r\n\r\n<table id=\"eip-id1169754088588\" style=\"width: 100%;\" summary=\"The expression 7\/8 plus 6.4 is given. The direction is given to \u201cChange 7\/8 to a decimal.\u201d To the right of this we have the long division problem with 8 dividing 7.000 and 0.875 as the quotient. Below 7.000 we have 64, a solid horizontal line, 60, 56, a solid horizontal line, 40, 40, a final horizontal line, and 0. The next direction is to \u201cAdd.\u201d To the right of this we have 0.875 + 6.4, so seven eighths plus 6.4 equals 7.275.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>\\(\\frac{7}{8}+6.4\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Change \\(\\frac{7}{8}\\) to a decimal.<\/td>\r\n<td><span id=\"eip-id1169749852706\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_019_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td><\/td>\r\n<td>\\(0.875+6.4\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>\\(7.275\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>So, \\(\\frac{7}{8}+6.4=7.275\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 12<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655229698\" data-type=\"problem\">\r\n<p id=\"fs-id1170654953761\">Simplify: \\(\\frac{3}{8}+4.9\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654984861\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170654928209\">5.275<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<h1>Key Concepts<\/h1>\r\n<ul id=\"fs-id1170655106869\" data-bullet-style=\"bullet\">\r\n \t<li><strong data-effect=\"bold\">Round a Decimal<\/strong>\r\n<ol id=\"fs-id1170655114584\" class=\"stepwise\" type=\"1\">\r\n \t<li>Locate the given place value and mark it with an arrow.<\/li>\r\n \t<li>Underline the digit to the right of the place value.<\/li>\r\n \t<li>Is this digit greater than or equal to 5? Yes\u2014add 1 to the digit in the given place value. No\u2014do <u data-effect=\"underline\">not<\/u> change the digit in the given place value.<\/li>\r\n \t<li>Rewrite the number, deleting all digits to the right of the rounding digit.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">Add or Subtract Decimals<\/strong>\r\n<ol id=\"fs-id1170655063011\" class=\"stepwise\" type=\"1\">\r\n \t<li>Write the numbers so the decimal points line up vertically.<\/li>\r\n \t<li>Use zeros as place holders, as needed.<\/li>\r\n \t<li>Add or subtract the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">Multiply Decimals<\/strong>\r\n<ol id=\"fs-id1170655162096\" class=\"stepwise\" type=\"1\">\r\n \t<li>Determine the sign of the product.<\/li>\r\n \t<li>Write in vertical format, lining up the numbers on the right. Multiply the numbers as if they were whole numbers, temporarily ignoring the decimal points.<\/li>\r\n \t<li>Place the decimal point. The number of decimal places in the product is the sum of the decimal places in the factors.<\/li>\r\n \t<li>Write the product with the appropriate sign.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">Multiply a Decimal by a Power of Ten<\/strong>\r\n<ol id=\"fs-id1170655037577\" class=\"stepwise\" type=\"1\">\r\n \t<li>Move the decimal point to the right the same number of places as the number of zeros in the power of 10.<\/li>\r\n \t<li>Add zeros at the end of the number as needed.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">Divide Decimals<\/strong>\r\n<ol id=\"fs-id1170655201026\" class=\"stepwise\" type=\"1\">\r\n \t<li>Determine the sign of the quotient.<\/li>\r\n \t<li>Make the divisor a whole number by \u201cmoving\u201d the decimal point all the way to the right. \u201cMove\u201d the decimal point in the dividend the same number of places - adding zeros as needed.<\/li>\r\n \t<li>Divide. Place the decimal point in the quotient above the decimal point in the dividend.<\/li>\r\n \t<li>Write the quotient with the appropriate sign.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">Convert a Decimal to a Proper Fraction<\/strong>\r\n<ol id=\"fs-id1170654983497\" class=\"stepwise\" type=\"1\">\r\n \t<li>Determine the place value of the final digit.<\/li>\r\n \t<li>Write the fraction: numerator\u2014the \u2018numbers\u2019 to the right of the decimal point; denominator\u2014the place value corresponding to the final digit.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">Convert a Fraction to a Decimal<\/strong> Divide the numerator of the fraction by the denominator.<\/li>\r\n<\/ul>\r\n<h1>1.4 Exercise Set<\/h1>\r\n<p id=\"fs-id1166422830559\">In the following exercises, round each number to the nearest tenth.<\/p>\r\n\r\n<ol class=\"twocolumn\">\r\n \t<li>0.67<\/li>\r\n \t<li>2.84<\/li>\r\n<\/ol>\r\n<p id=\"fs-id1170655041277\">In the following exercises, round each number to the nearest hundredth.<\/p>\r\n\r\n<ol class=\"twocolumn\" start=\"3\">\r\n \t<li>0.845<\/li>\r\n \t<li>0.299<\/li>\r\n \t<li>4.098<\/li>\r\n<\/ol>\r\n<div id=\"fs-id1170655041281\" data-type=\"exercise\">\r\n<div id=\"fs-id1170654965811\" data-type=\"problem\">In the following exercises, round each number to the nearest a) hundredth b) tenth c) whole number.<\/div>\r\n<ol class=\"twocolumn\" start=\"6\">\r\n \t<li data-type=\"problem\">5.781<\/li>\r\n \t<li data-type=\"problem\">63.479<\/li>\r\n<\/ol>\r\n<\/div>\r\n<p id=\"fs-id1166422576116\">In the following exercises, add or subtract.<\/p>\r\n\r\n<ol class=\"twocolumn\" start=\"8\">\r\n \t<li>\\(16.92+7.56\\)<\/li>\r\n \t<li>\\(21.76-30.99\\)<\/li>\r\n \t<li>\\(-16.53-24.38\\)<\/li>\r\n \t<li>\\(-38.69+31.47\\)<\/li>\r\n \t<li>\\(72.5-100\\)<\/li>\r\n \t<li>\\(15+0.73\\)<\/li>\r\n \t<li>\\(91.95-\\left(-10.462\\right)\\)<\/li>\r\n \t<li>\\(55.01-3.7\\)<\/li>\r\n \t<li>\\(2.51-7.4\\)<\/li>\r\n<\/ol>\r\n<p id=\"fs-id1166420388478\">In the following exercises, multiply.<\/p>\r\n\r\n<ol class=\"twocolumn\" start=\"17\">\r\n \t<li>\\(\\left(0.24\\right)\\left(0.6\\right)\\)<\/li>\r\n \t<li>\\(\\left(5.9\\right)\\left(7.12\\right)\\)<\/li>\r\n \t<li>\\(\\left(-4.3\\right)\\left(2.71\\right)\\)<\/li>\r\n \t<li>\\(\\left(-5.18\\right)\\left(-65.23\\right)\\)<\/li>\r\n \t<li>\\(\\left(0.06\\right)\\left(21.75\\right)\\)<\/li>\r\n \t<li>\\(\\left(9.24\\right)\\left(10\\right)\\)<\/li>\r\n \t<li>\\(\\left(55.2\\right)\\left(1000\\right)\\)<\/li>\r\n<\/ol>\r\n<div id=\"fs-id1170655084877\" data-type=\"exercise\">\r\n<div id=\"fs-id1170654983718\" data-type=\"problem\">In the following exercises, divide.<\/div>\r\n<ol class=\"twocolumn\" start=\"24\">\r\n \t<li data-type=\"problem\">\\(4.75\\div 25\\)<\/li>\r\n \t<li data-type=\"problem\">\\(\\$117.25\\div 48\\)<\/li>\r\n \t<li data-type=\"problem\">\\(0.6\\div 0.2\\)<\/li>\r\n \t<li data-type=\"problem\">\\(1.44\\div \\left(-0.3\\right)\\)<\/li>\r\n \t<li data-type=\"problem\">\\(-1.75\\div \\left(-0.05\\right)\\)<\/li>\r\n \t<li data-type=\"problem\">\\(5.2\\div 2.5\\)<\/li>\r\n \t<li data-type=\"problem\">\\(11\\div 0.55\\)<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div id=\"fs-id1170655228709\" data-type=\"exercise\">\r\n<h2><span style=\"font-weight: normal; text-align: initial; font-family: 'Times New Roman', Georgia, 'SBL Greek', serif; font-size: 14pt;\">In the following exercises, write each decimal as a fraction.<\/span><\/h2>\r\n<ol class=\"twocolumn\" start=\"31\">\r\n \t<li>0.04<\/li>\r\n \t<li>0.52<\/li>\r\n \t<li>1.25<\/li>\r\n \t<li>0.375<\/li>\r\n \t<li>0.095<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div id=\"fs-id1170655113928\" data-type=\"exercise\">\r\n<div id=\"fs-id1170655113931\" data-type=\"problem\">In the following exercises, convert each fraction to a decimal.<\/div>\r\n<ol class=\"twocolumn\" start=\"36\">\r\n \t<li data-type=\"problem\">\\(\\frac{17}{20}\\)<\/li>\r\n \t<li data-type=\"problem\">\\(\\frac{11}{4}\\)<\/li>\r\n \t<li data-type=\"problem\">\\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{310}{25}\\)<\/li>\r\n \t<li data-type=\"problem\">\\(\\frac{15}{11}\\)<\/li>\r\n \t<li data-type=\"problem\">\\(\\frac{15}{111}\\)<\/li>\r\n \t<li data-type=\"problem\">\\(2.4+\\frac{5}{8}\\)<\/li>\r\n<\/ol>\r\n<ol start=\"42\">\r\n \t<li><strong data-effect=\"bold\">Salary Increase.<\/strong> Marta got a raise and now makes \\$58,965.95 a year. Round this number to the nearest\r\na) dollar\r\nb) thousand dollars\r\nc) ten thousand dollars.<\/li>\r\n \t<li><strong data-effect=\"bold\">Sales Tax.<\/strong> Hyo Jin lives in Vancouver. She bought a refrigerator for \\$1,624.99 and when the clerk calculated the sales tax it came out to exactly \\$142.186625. Round the sales tax to the nearest\r\na) penny and\r\nb) dollar.<\/li>\r\n \t<li><strong data-effect=\"bold\">Paycheck.<\/strong> Annie has two jobs. She gets paid \\$14.04 per hour for tutoring at Community College and \\$8.75 per hour at a coffee shop. Last week she tutored for 8 hours and worked at the coffee shop for 15 hours.\r\na) How much did she earn?\r\nb) If she had worked all 23 hours as a tutor instead of working both jobs, how much more would she have earned?<\/li>\r\n<\/ol>\r\n<\/div>\r\n<span style=\"font-family: Helvetica, Arial, 'GFS Neohellenic', sans-serif; font-size: 1.2em; font-weight: bold;\">Glossary<\/span>\r\n<div class=\"textbox shaded\" data-type=\"glossary\">\r\n<dl id=\"fs-id1166425139638\">\r\n \t<dt>decimal<\/dt>\r\n \t<dd id=\"fs-id1166424911849\">A decimal is another way of writing a fraction whose denominator is a power of ten.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1166425061744\">\r\n \t<dt>repeating decimal<\/dt>\r\n \t<dd id=\"fs-id1166425061749\">A repeating decimal is a decimal in which the last digit or group of digits repeats endlessly.<\/dd>\r\n<\/dl>\r\n<\/div>\r\n<h1>Answers:<\/h1>\r\n<ol class=\"twocolumn\">\r\n \t<li>0.7<\/li>\r\n \t<li>2.8<\/li>\r\n \t<li>0.85<\/li>\r\n \t<li>0.30<\/li>\r\n \t<li>4.10<\/li>\r\n \t<li>a) 5.78 b) 5.8 c) 6<\/li>\r\n \t<li>a) 63.48 b) 63.5 c) 63<\/li>\r\n \t<li>24.48<\/li>\r\n \t<li>\\(-9.23\\)<\/li>\r\n \t<li>\\(-40.91\\)<\/li>\r\n \t<li>\\(-7.22\\)<\/li>\r\n \t<li>\\(-27.5\\)<\/li>\r\n \t<li>15.73<\/li>\r\n \t<li>102.212<\/li>\r\n \t<li>51.31<\/li>\r\n \t<li>\\(-4.89\\)<\/li>\r\n \t<li>0.144<\/li>\r\n \t<li>42.008<\/li>\r\n \t<li>\\(-11.653\\)<\/li>\r\n \t<li>337.8914<\/li>\r\n \t<li>1.305<\/li>\r\n \t<li>92.4<\/li>\r\n \t<li>55,200<\/li>\r\n \t<li>0.19<\/li>\r\n \t<li>\\$2.44<\/li>\r\n \t<li>3<\/li>\r\n \t<li>\\(-4.8\\)<\/li>\r\n \t<li>35<\/li>\r\n \t<li>2.08<\/li>\r\n \t<li>20<\/li>\r\n \t<li>\\(\\frac{1}{25}\\)<\/li>\r\n \t<li>\\(\\frac{13}{25}\\)<\/li>\r\n \t<li>\\(\\frac{5}{4}\\)<\/li>\r\n \t<li>\\(\\frac{3}{8}\\)<\/li>\r\n \t<li>\\(\\frac{19}{200}\\)<\/li>\r\n \t<li>0.85<\/li>\r\n \t<li>2.75<\/li>\r\n \t<li>\\(-12.4\\)<\/li>\r\n \t<li>\\(1.\\stackrel{\\text{\u2014}}{36}\\)<\/li>\r\n \t<li>\\(0.\\stackrel{\\text{\u2014}}{135}\\)<\/li>\r\n \t<li>3.025<\/li>\r\n \t<li>a) \\$58,966 b) \\$59,000 c) \\$60,000<\/li>\r\n \t<li>a) \\$142.19; b) \\$142<\/li>\r\n \t<li>a) \\$243.57 b) \\$79.35<\/li>\r\n<\/ol>\r\n<h1>Attributions<\/h1>\r\nThis chapter has been adapted from \u201cDecimals\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/elementary-algebra\"><em>Elementary Algebra<\/em><\/a> (OpenStax) by Lynn Marecek and MaryAnne Anthony-Smith, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>By the end of this section it is expected that you will be able to:<\/p>\n<ul>\n<li>Round decimals<\/li>\n<li>Add and subtract decimals<\/li>\n<li>Multiply and divide decimals<\/li>\n<li>Convert decimals, fractions, and percent<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p id=\"fs-id1170655162670\"><strong data-effect=\"bold\">Decimals<\/strong> are another way of writing <span class=\"no-emphasis\" data-type=\"term\">fraction<\/span>s whose denominators are powers of 10.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e7810cf57fcaffabf70908effb653dbc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#48;&#46;&#49;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#48;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#48;&#46;&#49;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#115;&#32;&#96;&#96;&#111;&#110;&#101;&#32;&#116;&#101;&#110;&#116;&#104;&#39;&#39;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#48;&#46;&#48;&#49;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#48;&#48;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#48;&#46;&#48;&#49;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#115;&#32;&#96;&#96;&#111;&#110;&#101;&#32;&#104;&#117;&#110;&#100;&#114;&#101;&#100;&#116;&#104;&#39;&#39;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#48;&#46;&#48;&#48;&#49;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#44;&#48;&#48;&#48;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#46;&#48;&#48;&#49;&#32;&#105;&#115;&#32;&#96;&#96;&#111;&#110;&#101;&#32;&#116;&#104;&#111;&#117;&#115;&#97;&#110;&#100;&#116;&#104;&#39;&#39;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#48;&#46;&#48;&#48;&#48;&#49;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#48;&#44;&#48;&#48;&#48;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#46;&#48;&#48;&#48;&#49;&#32;&#105;&#115;&#32;&#96;&#96;&#111;&#110;&#101;&#32;&#116;&#101;&#110;&#45;&#116;&#104;&#111;&#117;&#115;&#97;&#110;&#100;&#116;&#104;&#39;&#39;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"93\" width=\"459\" style=\"vertical-align: -42px;\" \/><\/p>\n<p id=\"fs-id1170655082460\">Notice that \u201cten thousand\u201d is a number larger than one, but \u201cone ten-thousand<strong data-effect=\"bold\">th<\/strong>\u201d is a number smaller than one. The \u201cth\u201d at the end of the name tells you that the number is smaller than one.<\/p>\n<p>When we name a whole number, the name corresponds to the place value based on the powers of ten. We read 10,000 as \u201cten thousand\u201d and 10,000,000 as \u201cten million.\u201d Likewise, the names of the <span class=\"no-emphasis\" data-type=\"term\">decimal<\/span> places correspond to their fraction values. <a class=\"autogenerated-content\" href=\"#figure1\">Figure 1<\/a> shows the names of the <span class=\"no-emphasis\" data-type=\"term\">place values<\/span> to the left and right of the decimal point.<\/p>\n<div id=\"CNX_ElemAlg_Figure_01_07_001_new\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">Place value of decimal numbers are shown to the left and right of the decimal point.<a id=\"figure1\"><\/a><\/div>\n<figure style=\"width: 286px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_001_new.jpg\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_001_new.jpg\" alt=\"A table is shown with the title Place Value. From left to right the row reads \u201cHundred thousands,\u201d \u201cTen thousands,\u201d \u201cThousands,\u201d \u201cHundreds,\u201d \u201cTens,\u201d and \u201cOnes.\u201d Then there is a blank cell and below it is a decimal point. To the right of this, the cells read \u201cTenths,\u201d \u201cHundredths,\u201d \u201cThousandths,\u201d \u201cTen-thousandths,\u201d and \u201cHundred-thousandths.\u201d\" width=\"286\" height=\"260\" data-media-type=\"image\/jpeg\" \/><\/a><figcaption class=\"wp-caption-text\">Figure 1<\/figcaption><\/figure>\n<\/div>\n<h1>Round Decimals<\/h1>\n<p id=\"fs-id1170654977720\">Rounding decimals is very much like rounding whole numbers. We will round decimals with a method based on the one we used to round whole numbers.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"title\">Round 18.379 to the nearest hundredth.<\/div>\n<div id=\"fs-id1170654965636\" data-type=\"exercise\">\n<div id=\"fs-id1170655213305\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p><span id=\"fs-id1170655218662\" data-type=\"media\" data-alt=\"A table is given with four steps. The first step reads \u201cStep 1: Locate the given place value and mark it with an arrow.\u201d To the right of this, we have the number 18.379; above it, are the words hundreds place, which has an arrow pointing to the 7.\"><img decoding=\"async\" title=\"A table is given with four steps. The first step reads \u201cStep 1: Locate the given place value and mark it with an arrow.\u201d To the right of this, we have the number 18.379; above it, are the words hundreds place, which has an arrow pointing to the 7.\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_004a_new.jpg\" alt=\"A table is given with four steps. The first step reads \u201cStep 1: Locate the given place value and mark it with an arrow.\u201d To the right of this, we have the number 18.379; above it, are the words hundreds place, which has an arrow pointing to the 7.\" data-media-type=\"image\/jpeg\" data-popupalt-original-title=\"null\" \/><\/span><span id=\"fs-id1170653985218\" data-type=\"media\" data-alt=\"The second step reads \u201cStep 2. Underline the digit to the right of the given place value.\u201d To the right of this, we have 18.379 with the 9 underlined.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_004b_new.jpg\" alt=\"The second step reads \u201cStep 2. Underline the digit to the right of the given place value.\u201d To the right of this, we have 18.379 with the 9 underlined.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170653901496\" data-type=\"media\" data-alt=\"The third step reads \u201cStep 3. Is this digit greater than or equal to 5? Below this reads, \u201cYes: add 1 to the digit in the given place value.\u201d Below this reads, \u201cNo: do not change the digit in the given place value.\u201d To the right of this, it says \u201cBecause 9 is greater than or equal to \u201d To the right of this, we have the number 18.379 with the 9 marked \u201cdelete\u201d and the 7 marked \u201cadd 1.\u201d\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_004c_new.jpg\" alt=\"The third step reads \u201cStep 3. Is this digit greater than or equal to 5? Below this reads, \u201cYes: add 1 to the digit in the given place value.\u201d Below this reads, \u201cNo: do not change the digit in the given place value.\u201d To the right of this, it says \u201cBecause 9 is greater than or equal to \u201d To the right of this, we have the number 18.379 with the 9 marked \u201cdelete\u201d and the 7 marked \u201cadd 1.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170653744228\" data-type=\"media\" data-alt=\"Finally, the last step reads \u201cStep 4. Rewrite the number, removing all digits to the right of the rounding digit.\u201d To the right of this, we have 18.38 followed by \u201c18.38 is 18.379 rounded to the nearest hundredth.\u201d\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_004d_new.jpg\" alt=\"Finally, the last step reads \u201cStep 4. Rewrite the number, removing all digits to the right of the rounding digit.\u201d To the right of this, we have 18.38 followed by \u201c18.38 is 18.379 rounded to the nearest hundredth.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1170654954676\">Round to the nearest hundredth: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-83eae1c19a0657fca24cebaed5b04b08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#48;&#52;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"40\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655195781\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654903945\">1.05<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170655029280\">We summarize the steps for rounding a <span class=\"no-emphasis\" data-type=\"term\">decimal<\/span> here.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Round Decimals<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1166424888811\" class=\"stepwise\" type=\"1\">\n<li>Locate the given place value and mark it with an arrow.<\/li>\n<li>Underline the digit to the right of the place value.<\/li>\n<li>Is this digit greater than or equal to 5?\n<ul data-bullet-style=\"bullet\">\n<li>Yes\u2014add 1 to the digit in the given place value.<\/li>\n<li>No\u2014do <u data-effect=\"underline\">not<\/u> change the digit in the given place value.<\/li>\n<\/ul>\n<\/li>\n<li>Rewrite the number, deleting all digits to the right of the rounding digit.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1170653237730\" class=\"howto\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Round 18.379 to the nearest a) tenth b) whole number.<\/p>\n<div id=\"fs-id1170654872675\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1170654935270\">Round 18.379<\/p>\n<p>a) to the nearest tenth<\/p>\n<table id=\"eip-id1169752878832\" style=\"width: 100%;\" summary=\"A table is given with four steps. The first step reads \u201cLocate the tenths place and mark it with an arrow.\u201d To the right of this, we have the number 18.379; below it is written tenths place, which has an arrow pointing to the 3. The second step reads \u201cUnderline the digit to the right of the tenths digit.\u201d To the right of this, we have 18.379 with the 7 underlined. The third step reads \u201cBecause 7 is greater than or equal to 5, add 1 to the 3.\u201d To the right of this, we have the number 18.379 with the 7 and 9 marked \u201cdelete\u201d and the 3 marked \u201cadd 1.\u201d Finally, the last step reads \u201cRewrite the number, deleting all digits to the right of the tenths place.\u201d To the right of this, we have 18.4 followed by \u201cSo, 18.379 rounded to the nearest tenth is 18.4.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>Locate the tenths place with an arrow.<\/td>\n<td><span id=\"eip-id1169752964044\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_005a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Underline the digit to the right of the given place value.<\/td>\n<td><span id=\"eip-id1169752799574\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_005b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Because 7 is greater than or equal to 5, add 1 to the 3.<\/td>\n<td><span id=\"eip-id1169750840488\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_005c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Rewrite the number, deleting all digits to the right of the rounding digit.<\/td>\n<td><span id=\"eip-id1169750591270\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_005d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Notice that the deleted digits were NOT replaced with zeros.<\/td>\n<td>So, 18.379 rounded to the nearest tenth is 18.4.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>b) to the nearest whole number<\/p>\n<table id=\"eip-id1169754002832\" style=\"width: 100%;\" summary=\"A table is given with four steps. The first step reads \u201cLocate the ones place and mark it with an arrow.\u201d To the right of this, we have the number 18.379; below it is written ones place, which has an arrow pointing to the 8. The second step reads \u201cUnderline the digit to the right of the ones place.\u201d To the right of this, we have 18.379 with the 3 underlined. The third step reads \u201cSince 3 is not greater than or equal to 5, do not add 1 to the 8.\u201d To the right of this, we have the number 18.379 with the 3, 7, and 9 marked \u201cdelete\u201d and the 8 marked \u201cdo not add 1.\u201d Finally, the last step reads \u201cRewrite the number, deleting all digits to the right of the ones place.\u201d To the right of this, we have 18 followed by \u201cSo 18.379 rounded to the nearest whole number is 18.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>Locate the ones place with an arrow.<\/td>\n<td><span id=\"eip-id1169754058794\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_006a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Underline the digit to the right of the given place value.<\/td>\n<td><span id=\"eip-id1169754058811\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_006b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Since 3 is not greater than or equal to 5, do not add 1 to the 8.<\/td>\n<td><span id=\"eip-id1169754362233\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_006c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Rewrite the number, deleting all digits to the right of the rounding digit.<\/td>\n<td><span id=\"eip-id1169754362250\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_006d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>So, 18.379 rounded to the nearest whole number is 18.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655025740\" data-type=\"problem\">\n<p>Round <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7195cbc57fc89ea93f94d2f085cf2aac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#46;&#53;&#56;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"40\" style=\"vertical-align: 0px;\" \/> to the nearest a) hundredth b) tenth c) whole number.<\/p>\n<\/div>\n<div id=\"fs-id1170655105998\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p>a) 6.58 b) 6.6 c) 7<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Add and Subtract Decimals<\/h1>\n<p id=\"fs-id1170655154216\">To add or subtract decimals, we line up the decimal points. By lining up the decimal points this way, we can add or subtract the corresponding <span class=\"no-emphasis\" data-type=\"term\">place values<\/span>. We then add or subtract the numbers as if they were whole numbers and then place the decimal point in the sum.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Add or Subtract Decimals<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1166422560823\" class=\"stepwise\" type=\"1\">\n<li>Write the numbers so the decimal points line up vertically.<\/li>\n<li>Use zeros as place holders, as needed.<\/li>\n<li>Add or subtract the numbers as if they were whole numbers. Then place the decimal point in the answer under the decimal points in the given numbers.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div class=\"howto\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1170654982792\">Add: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9991789d03a7c33aed0761ff0e23b447_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#51;&#46;&#53;&#43;&#52;&#49;&#46;&#51;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"94\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654944111\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-474\" style=\"height: 90px;\" summary=\".\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 487.406px;\">Write the numbers so the decimal points line up vertically.<\/td>\n<td style=\"height: 14px; width: 761.406px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ae71b3960a616ad535801221d32eaa31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#117;&#110;&#100;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#55;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#51;&#46;&#53;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#43;&#52;&#49;&#46;&#51;&#56;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"71\" style=\"vertical-align: -20px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 46px;\">\n<td style=\"height: 46px; width: 487.406px;\">Put 0 as a placeholder after the 5 in 23.5.<br \/>\nRemember, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3f1b899e8ab62b25b4d60883bb93427b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#49;&#48;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#48;&#125;&#123;&#49;&#48;&#48;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#111;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#48;&#46;&#53;&#61;&#48;&#46;&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"176\" style=\"vertical-align: -7px;\" \/>.<\/td>\n<td style=\"height: 46px; width: 761.406px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7f760ef6945cf952e671c57b1a5f0adb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#117;&#110;&#100;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#55;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#51;&#46;&#53;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#43;&#52;&#49;&#46;&#51;&#56;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#125;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"71\" style=\"vertical-align: -19px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"height: 30px; width: 487.406px;\">Add the numbers as if they were whole numbers.<br \/>\nThen place the decimal point in the sum.<\/td>\n<td style=\"height: 30px; width: 761.406px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2df271144080e55f8a495eb1f9e2c4ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#117;&#110;&#100;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#55;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#51;&#46;&#53;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#43;&#52;&#49;&#46;&#51;&#56;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#55;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#54;&#52;&#46;&#56;&#56;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"61\" width=\"71\" style=\"vertical-align: -24px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655114138\" data-type=\"problem\">\n<p id=\"fs-id1170655213420\">Add: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-00f0142b4830751ba2b6594539d2c3e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#46;&#56;&#43;&#49;&#49;&#46;&#54;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"85\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654919229\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655167053\">16.49<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170653235826\" class=\"try\" data-type=\"note\">\n<div data-type=\"exercise\">\n<div id=\"fs-id1170655208527\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654921340\" data-type=\"problem\">\n<p id=\"fs-id1170655162342\">Subtract: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b67becbfec305cc9ec97e1830ee2f4b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#45;&#49;&#52;&#46;&#54;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"79\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655067989\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-645\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b67becbfec305cc9ec97e1830ee2f4b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#45;&#49;&#52;&#46;&#54;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"79\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Write the numbers so the decimal points line up vertically.<br \/>\nRemember, 20 is a whole number, so place the decimal point after the 0.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f5edfc958269163ff366cf81d72c36e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#117;&#110;&#100;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#55;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#48;&#46;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#45;&#49;&#52;&#46;&#54;&#53;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"71\" style=\"vertical-align: -20px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Put in zeros to the right as placeholders.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c4c76f769eb03597392f135ef7c591eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#55;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#48;&#46;&#48;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#117;&#110;&#100;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#45;&#49;&#52;&#46;&#54;&#53;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"55\" style=\"vertical-align: -15px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Subtract and place the decimal point in the answer.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ac4fa1242ecef6978540a712feecbdec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#117;&#110;&#100;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#56;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#49;&#125;&#123;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#50;&#125;&#125;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#57;&#125;&#123;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#49;&#48;&#125;&#125;&#125;&#123;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#48;&#125;&#125;&#46;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#57;&#125;&#123;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#49;&#48;&#125;&#125;&#125;&#123;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#48;&#125;&#125;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#49;&#48;&#125;&#125;&#123;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#48;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#46;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#54;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#53;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#46;&#56;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#46;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#53;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"92\" width=\"124\" style=\"vertical-align: -40px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654965912\" data-type=\"problem\">\n<p id=\"fs-id1170655215425\">Subtract: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b7091da98fe77e667046f8c4e8b71db3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#45;&#57;&#46;&#53;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"70\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655226477\">0.42<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Multiply and Divide Decimals<\/h1>\n<p id=\"fs-id1170655129811\">Multiplying decimals is very much like multiplying whole numbers\u2014we just have to determine where to place the decimal point. The procedure for multiplying decimals will make sense if we first convert them to fractions and then multiply.<\/p>\n<p id=\"fs-id1170655215976\">So let\u2019s see what we would get as the <span class=\"no-emphasis\" data-type=\"term\">product<\/span> of decimals by converting them to fractions first. We will do two examples side-by-side. Look for a pattern!<\/p>\n<table id=\"eip-id1169754130025\" style=\"width: 100%;\" summary=\"The numbers 0.3, 0.7, 0.2, and 0.46 are shown, with the first three all marked \u201c1 place\u201d and 0.46 marked \u201c2 places.\u201d Below this line, the instruction \u201cConvert to fractions\u201d is given. We have 3\/10 times 7\/10 and 2\/10 times 46\/100. Note that these fractions correspond to the numbers given above. Then the instruction is given to multiply the numbers, so we have 21\/100 and 92\/1000. The next line instructs us to \u201cConvert to decimals.\u201d We are left with 0.21, which is marked as having \u201c2 places,\u201d and 0.092, which is marked as having \u201c3 places.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1169754130042\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_009a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">Convert to fractions.<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2c539148683ba11410ba46f819d41cc7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#56;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"1\" width=\"1\" style=\"vertical-align: 0px;\" \/><\/td>\n<td><span id=\"eip-id1169753944283\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_009b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1169753944299\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_009c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Convert to decimals.<\/td>\n<td><span id=\"eip-id1169753944316\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_009d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170655162411\">Notice, in the first example, we multiplied two numbers that each had one digit after the decimal point and the product had two decimal places. In the second example, we multiplied a number with one decimal place by a number with two decimal places and the product had three decimal places.<\/p>\n<p id=\"fs-id1170655062737\">We multiply the numbers just as we do whole numbers, temporarily ignoring the decimal point. We then count the number of decimal points in the factors and that sum tells us the number of decimal places in the product.<\/p>\n<p id=\"fs-id1170655029564\">The rules for multiplying positive and negative numbers apply to decimals, too, of course!<\/p>\n<p id=\"fs-id1170655121723\">When <em data-effect=\"italics\">multiplying<\/em> two numbers,<\/p>\n<ul id=\"fs-id1170655188642\" data-bullet-style=\"bullet\">\n<li>if their signs are the <em data-effect=\"italics\">same<\/em> the product is <em data-effect=\"italics\">positive<\/em>.<\/li>\n<li>if their signs are <em data-effect=\"italics\">different<\/em> the product is <em data-effect=\"italics\">negative<\/em>.<\/li>\n<\/ul>\n<p id=\"fs-id1170655028705\">When we multiply signed decimals, first we determine the sign of the product and then multiply as if the numbers were both positive. Finally, we write the product with the appropriate sign.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Multiply Decimals<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1166424905197\" class=\"stepwise\" type=\"1\">\n<li>Determine the sign of the product.<\/li>\n<li>Write in vertical format, lining up the numbers on the right. Multiply the numbers as if they were whole numbers, temporarily ignoring the decimal points.<\/li>\n<li>Place the decimal point. The number of decimal places in the product is the sum of the number of decimal places in the factors.<\/li>\n<li>Write the product with the appropriate sign.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1170654988259\" class=\"howto\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655075135\" data-type=\"problem\">\n<p id=\"fs-id1170655208074\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f32062cf05fccef29f13ce095a5bca24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#46;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#46;&#48;&#55;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"106\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655111654\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1169753348487\" style=\"width: 100%;\" summary=\"The expression 3.9 times 4.075 is given. A table is given with descriptions of steps on the left and the mathematical work on the right. The first step reads \u201cDetermine the sign of the product. The signs are the same.\u201d To the right of this, we have \u201cThe product will be positive.\u201d The second step reads \u201cWrite the numbers in vertical format, lining up the numbers on the right.\u201d To the right of this, we have 4.075 on one line, and below it we have the times symbol followed by 3.9. The numbers are aligned on their right, so 5 is above 9. Then, there is a solid horizontal line below our numbers. Then the third step reads \u201cMultiply the numbers as if they were whole numbers, temporarily ignoring the decimal points.\u201d We again have 4.075 on one line, and below it we have the times symbol followed by 3.9. The numbers are again aligned on their right, so 5 is above 9, there is a solid horizontal line below our numbers. Now, there are other numbers underneath this line: specifically, the number 36675 and below that there is the number 12225, which is shifted over one space so that the 7 from 36675 lines up with the 5 from 12225. Below these numbers there is another solid horizontal line, below which there is the number 158925. Then the fourth step reads \u201cPlace the decimal points. Add the number of decimal places in the factors (1 plus 3). Place the decimal point 4 places from the right.\u201d To the right of this, we have the same setup as in the previous line, however, the number 4.075 is marked \u201c3 places,\u201d the number 3.9 is marked \u201c1 place,\u201d and the number 158925 is marked \u201c4 places.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td>(\u22123.9)(4.075)<\/td>\n<\/tr>\n<tr>\n<td>The signs are different. The product will be negative.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write in vertical format, lining up the numbers on the right.<\/td>\n<td><span id=\"eip-id1169752872718\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_010b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1169750874908\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_010c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add the number of decimal places in the factors (1 + 3).<\/p>\n<p><span id=\"eip-id1169753269067\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_010a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><br \/>\nPlace the decimal point 4 places from the right.<\/td>\n<td><span id=\"eip-id1169753284625\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_010d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>The signs are different, so the product is negative.<\/td>\n<td>(\u22123.9)(4.075) = \u221215.8925<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655057717\" data-type=\"problem\">\n<p id=\"fs-id1170655083436\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4a7a441eadbd1257d757bec046adadb7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#46;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#46;&#49;&#48;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"92\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655025662\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655037473\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9357cbeb9d25deb71ef36193f8a83c18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#55;&#46;&#52;&#56;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"71\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170655107014\">In many of your other classes, especially in the sciences, you will multiply decimals by powers of 10 (10, 100, 1000, etc.). If you multiply a few products on paper, you may notice a pattern relating the number of zeros in the power of 10 to number of decimal places we move the decimal point to the right to get the product.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Multiply a Decimal by a Power of Ten<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1166422556911\" class=\"stepwise\" type=\"1\">\n<li>Move the decimal point to the right the same number of places as the number of zeros in the power of 10.<\/li>\n<li>Add zeros at the end of the number as needed.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1170654972139\" class=\"howto\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654981723\" data-type=\"problem\">\n<p id=\"fs-id1170655088072\">Multiply 5.63 a) by 10 b) by 100 c) by 1,000.<\/p>\n<\/div>\n<div id=\"fs-id1170655174581\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1170654915804\">By looking at the number of zeros in the multiple of ten, we see the number of places we need to move the decimal to the right.<\/p>\n<p id=\"fs-id1166424779193\">a)<\/p>\n<table id=\"eip-id1169752865183\" style=\"width: 100%;\" summary=\"The expression 5.63 times 10 is given. The directions read \u201cThere is 1 zero in 10, so move the decimal point 1 place to the right.\u201d The number 5.63 is shown with an arrow starting from the decimal point and moving to the space between 6 and 3. Then the number 56.3 is given.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td>5.63(10)<\/td>\n<\/tr>\n<tr>\n<td>There is 1 zero in 10, so move the decimal point 1 place to the right.<\/td>\n<td><span id=\"eip-id1169753258712\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_011_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>b)<\/p>\n<table id=\"eip-id1169752935718\" style=\"width: 100%;\" summary=\"The expression 5.63 times 100 is given. The directions read \u201cThere are 2 zeros in 100, so move the decimal point 2 places to the right.\u201d The number 5.63 is shown with an arrow starting from the decimal point, moving to the space between 6 and 3, and then moving further to the space after 3. Then the number 563 is given.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td>5.63(100)<\/td>\n<\/tr>\n<tr>\n<td>There are 2 zeros in 100, so move the decimal point 2 places to the right.<\/td>\n<td><span id=\"eip-id1169752908904\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_012_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>c)<\/p>\n<table id=\"eip-id1169751883861\" style=\"width: 100%;\" summary=\"The expression 5.63 times 1,000 is given. The directions read \u201cThere are 3 zeros in 1,000, so move the decimal point 3 places to the right.\u201d The number 5.63 is shown with an arrow starting from the decimal point, moving to the space between 6 and 3, moving further to the space after 3, and then moving one space over from that space. The directions read \u201cA zero must be added at the end.\u201d Then the number 5,630 is given.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td>5.63(1,000)<\/td>\n<\/tr>\n<tr>\n<td>There are 3 zeros in 1,000, so move the decimal point 3 places to the right.<\/td>\n<td><span id=\"eip-id1169749465627\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_013a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>A zero must be added at the end.<\/td>\n<td><span id=\"eip-id1169754029608\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_013b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655150426\" data-type=\"problem\">\n<p id=\"fs-id1170655089696\">Multiply 2.58 a) by 10 b) by 100 c) by 1,000.<\/p>\n<\/div>\n<div id=\"fs-id1170654981785\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655196937\">a) 25.8 b) 258 c) 2,580<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p>Just as with multiplication, division of decimals is very much like dividing whole numbers. We just have to figure out where the decimal point must be placed.<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1170654953534\">To divide decimals, determine what power of 10 to multiply the denominator by to make it a whole number. Then multiply the numerator by that same power of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5450913cc453faf132dc56e5965ca797_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/>. Because of the equivalent fractions property, we haven\u2019t changed the value of the fraction! The effect is to move the decimal points in the numerator and denominator the same number of places to the right. For example:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-37d9908fe058e586c8136061a45f04f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#48;&#46;&#56;&#125;&#123;&#48;&#46;&#52;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#48;&#46;&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#123;&#48;&#46;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#52;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"72\" width=\"43\" style=\"vertical-align: -31px;\" \/><\/p>\n<p id=\"fs-id1170654941815\">We use the rules for dividing positive and negative numbers with decimals, too. When dividing signed decimals, first determine the sign of the quotient and then divide as if the numbers were both positive. Finally, write the quotient with the appropriate sign.<\/p>\n<p id=\"fs-id1170655133056\">We review the notation and vocabulary for division:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4f1069ae58a4801776787f951bb87297_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#100;&#105;&#118;&#105;&#100;&#101;&#110;&#100;&#125;&#125;&#123;&#97;&#125;&#92;&#100;&#105;&#118;&#32;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#100;&#105;&#118;&#105;&#115;&#111;&#114;&#125;&#125;&#123;&#98;&#125;&#61;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#113;&#117;&#111;&#116;&#105;&#101;&#110;&#116;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#99;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#100;&#105;&#118;&#105;&#115;&#111;&#114;&#125;&#125;&#123;&#98;&#125;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#113;&#117;&#111;&#116;&#105;&#101;&#110;&#116;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#99;&#125;&#125;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#100;&#105;&#118;&#105;&#100;&#101;&#110;&#100;&#125;&#125;&#123;&#97;&#125;&#125;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"53\" width=\"384\" style=\"vertical-align: -25px;\" \/><\/p>\n<p id=\"fs-id1170654928702\">We\u2019ll write the steps to take when dividing decimals, for easy reference.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Divide Decimals<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1166422823773\" class=\"stepwise\" type=\"1\">\n<li>Determine the sign of the quotient.<\/li>\n<li>Make the divisor a whole number by \u201cmoving\u201d the decimal point all the way to the right. \u201cMove\u201d the decimal point in the dividend the same number of places\u2014adding zeros as needed.<\/li>\n<li>Divide. Place the decimal point in the quotient above the decimal point in the dividend.<\/li>\n<li>Write the quotient with the appropriate sign.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1170655089296\" class=\"howto\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654962371\" data-type=\"problem\">\n<p id=\"fs-id1170654935439\">Divide: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8488c99620218d817e5fa00961852a72_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#53;&#46;&#53;&#54;&#92;&#100;&#105;&#118;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#48;&#46;&#48;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"134\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654969632\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1170655041701\">Remember, you can \u201cmove\u201d the decimals in the divisor and dividend because of the Equivalent Fractions Property.<\/p>\n<table id=\"eip-id1169754369321\" style=\"height: 288px; width: 100%;\" summary=\"The expression negative 25.65 divided by negative 0.06 is given. A table is given with directions on the left and the mathematical steps on the right. The first step reads \u201cThe signs are the same.\u201d To the right of this, we have \u201cThe quotient is positive.\u201d The second and third steps, respectively, read \u201cMake the divisor a whole number by &#96;moving\u2019 the decimal point all the way to the right\u201d and \u201cMove the decimal point in the dividend the same number of places.\u201d To the right of this, we have a long division problem set up with 0.06 dividing 25.65, but for both 0.06 and 25.65 there are arrows from the decimal points to the space after the last number. The fourth step reads \u201cDivide. Place the decimal point in the quotient above the decimal point in the dividend.\u201d To the right of this, we have a long division problem set up with 006. Dividing 2565.0. The quotient is given as 427.5. To show the work, below 2565.0, it reads negative 24, solid horizontal line, 16, negative 12, solid horizontal line, 45, negative 42, solid horizontal line, 30, 30, and a final solid horizontal line. The fifth step reads \u201cWrite the quotient with the appropriate sign.\u201d To the right of this, we have negative 25.65 divided by negative 0.06 equals 427.5.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 16px;\">\n<td style=\"height: 16px; width: 413.203px;\"><\/td>\n<td style=\"height: 16px; width: 221.016px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6c5d0155cc7f9b63740eca2e053e939a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#53;&#46;&#54;&#53;&#92;&#100;&#105;&#118;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#48;&#46;&#48;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"134\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"height: 16px; width: 413.203px;\">The signs are the same.<\/td>\n<td style=\"height: 16px; width: 221.016px;\">The quotient is positive.<\/td>\n<\/tr>\n<tr style=\"height: 32px;\">\n<td style=\"height: 32px; width: 413.203px;\">Make the divisor a whole number by \u201cmoving\u201d the decimal point all the way to the right.<\/td>\n<td style=\"height: 32px; width: 221.016px;\"><\/td>\n<\/tr>\n<tr style=\"height: 32px;\">\n<td style=\"height: 32px; width: 413.203px;\">\u201cMove\u201d the decimal point in the dividend the same number of places.<\/td>\n<td style=\"height: 32px; width: 221.016px;\"><span id=\"eip-id1169751952546\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_014a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 160px;\">\n<td style=\"height: 160px; width: 413.203px;\">Divide.<br \/>\nPlace the decimal point in the quotient above the decimal point in the dividend.<\/td>\n<td style=\"height: 160px; width: 221.016px;\"><span id=\"eip-id1169751952565\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_014b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 32px;\">\n<td style=\"height: 32px; width: 413.203px;\">Write the quotient with the appropriate sign.<\/td>\n<td style=\"height: 32px; width: 221.016px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-92947425befdea80376871be61a6b541_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#53;&#46;&#54;&#53;&#92;&#100;&#105;&#118;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#48;&#46;&#48;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#52;&#50;&#55;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"198\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655353521\" data-type=\"problem\">\n<p id=\"fs-id1170655230047\">Divide: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c3c7c009bdfc4a06524129344bea244_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#51;&#46;&#52;&#57;&#50;&#92;&#100;&#105;&#118;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#48;&#46;&#48;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"143\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654931861\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655351826\">587.3<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170655124340\">A common application of dividing whole numbers into decimals is when we want to find the price of one item that is sold as part of a multi-pack. For example, suppose a case of 24 water bottles costs &#36;3.99. To find the price of one water bottle, we would divide &#36;3.99 by 24. We show this division in the next example. In calculations with money, we will round the answer to the nearest cent (hundredth).<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654938076\" data-type=\"problem\">\n<p id=\"fs-id1170654981962\">Divide: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-110c389ee4c7a9415e1aed26488f241e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#36;&#51;&#46;&#57;&#57;&#92;&#100;&#105;&#118;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"80\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655133913\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1169754137615\" class=\"unnumbered unstyled can-break\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-110c389ee4c7a9415e1aed26488f241e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#36;&#51;&#46;&#57;&#57;&#92;&#100;&#105;&#118;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"80\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Place the decimal point in the quotient above the decimal point in the dividend.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Divide as usual.<br \/>\nWhen do we stop? Since this division involves money, we round it to the nearest cent (hundredth.) To do this, we must carry the division to the thousandths place.<\/td>\n<td><span id=\"eip-id1169754122161\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_015_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Round to the nearest cent.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d163877b1e8c0b766b3b96e7ef3d71e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#36;&#48;&#46;&#49;&#54;&#54;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#92;&#36;&#48;&#46;&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"114\" style=\"vertical-align: -1px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7eca36918eaa0c82eb3c0094f34970c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#36;&#51;&#46;&#57;&#57;&#92;&#100;&#105;&#118;&#32;&#50;&#52;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#92;&#36;&#48;&#46;&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"144\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655104719\" data-type=\"problem\">\n<p id=\"fs-id1170654943489\">Divide: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-144da9f609fcedb1149586d26614e9e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#36;&#54;&#46;&#57;&#57;&#92;&#100;&#105;&#118;&#32;&#51;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"80\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654983050\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655354181\">&#36;0.19<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Convert Decimals and Fractions<\/h1>\n<p id=\"fs-id1170654915544\">We convert decimals into fractions by identifying the place value of the last (farthest right) digit. In the decimal 0.03 the 3 is in the hundredths place, so 100 is the denominator of the fraction equivalent to 0.03<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1a5e5a8366c3507765b1f608a41091d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#48;&#46;&#48;&#51;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#49;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"91\" style=\"vertical-align: -7px;\" \/><\/p>\n<p id=\"fs-id1170655205009\">Notice, when the number to the left of the decimal is zero, we get a fraction whose numerator is less than its denominator. Fractions like this are called <span class=\"no-emphasis\" data-type=\"term\">proper fractions<\/span>.<\/p>\n<p id=\"fs-id1170655197111\">The steps to take to convert a decimal to a fraction are summarized in the procedure box.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Covert a Decimal to a Proper Fraction<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1166422823849\" class=\"stepwise\" type=\"1\">\n<li>Determine the place value of the final digit.<\/li>\n<li>Write the fraction.\n<ul id=\"fs-id1170655121293\" data-bullet-style=\"bullet\">\n<li>numerator\u2014the \u201cnumbers\u201d to the right of the decimal point<\/li>\n<li>denominator\u2014the place value corresponding to the final digit<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1170655206712\" class=\"howto\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655150644\" data-type=\"problem\">\n<p id=\"fs-id1170654986180\">Write 0.374 as a fraction.<\/p>\n<\/div>\n<div id=\"fs-id1170655205678\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-id1169752838117\" style=\"width: 100%;\" summary=\"The number 0.374 is given. A table is given with directions on the left and the mathematical steps on the right. The first step reads \u201cDetermine the place value of the final digit.\u201d To the right of this, we have 0.3 marked as tenths, 7 marked as hundredths, and 4 marked as thousandths. The second step reads \u201cWrite the fraction: The numerator is 374.\u201d To the right of this, we have 374\/1,000. The third step reads \u201cSimplify the fraction.\u201d To the right of this, we have the quantity (2 times 187) divided by the quantity (2 times 500). The fourth step reads \u201cDivide out the common factors.\u201d To the right of this, we have 187\/500. So 0.374 equals 187 over 500.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6fb72f5a72eca5b99b44cb6e7adebb70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#51;&#55;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"41\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Determine the place value of the final digit.<\/td>\n<td data-align=\"center\"><span id=\"eip-id1169752926445\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_016_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write the fraction for 0.374:<\/p>\n<ul id=\"eip-id1169752926531\" data-bullet-style=\"\">\n<li>The numerator is 374.<\/li>\n<li>The denominator is 1,000.<\/li>\n<\/ul>\n<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5616e26a0627c5b2e53f0670ec4d4991_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#55;&#52;&#125;&#123;&#49;&#48;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"28\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify the fraction.<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-880a22a42e6c063f34365c8276874415_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#56;&#55;&#125;&#123;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#53;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"32\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Divide out the common factors.<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3c9cab8fa98c7915b1aae25701bb1a79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#56;&#55;&#125;&#123;&#53;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"21\" style=\"vertical-align: -6px;\" \/><br \/>\nso, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7841db4eb8141fd96434a3d8a88f3999_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#51;&#55;&#52;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#56;&#55;&#125;&#123;&#53;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"87\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170654965315\">Did you notice that the number of zeros in the denominator of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f5a0b0b84031fca829bd1074954eb741_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#55;&#52;&#125;&#123;&#49;&#44;&#48;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"32\" style=\"vertical-align: -9px;\" \/> is the same as the number of decimal places in 0.374?<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655351640\" data-type=\"problem\">\n<p>Write 0.234 as a fraction.<\/p>\n<\/div>\n<div id=\"fs-id1170655158112\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655125808\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7fea94e81c9c8d72801aa04b0d626041_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#49;&#55;&#125;&#123;&#53;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"21\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p>We\u2019ve learned to convert decimals to fractions. Now we will do the reverse\u2014convert fractions to decimals. Remember that the fraction bar means division. So <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c995a9c919f066bf6863b7f22d9cc88f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> can be written <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aded24d762999503baa13a9b6c56c4f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#100;&#105;&#118;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"39\" style=\"vertical-align: -1px;\" \/> or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-08ae81aa7e2a21e0983de563a816cb66_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"25\" style=\"vertical-align: -5px;\" \/>. This leads to the following method for converting a fraction to a decimal.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Covert a Fraction to a Decimal<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>To convert a fraction to a decimal, divide the numerator of the fraction by the denominator of the fraction.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170655222662\" class=\"howto\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655150719\" data-type=\"problem\">\n<p id=\"fs-id1170655105604\">Write <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-01dd0e273e62ac56a29d412e5f5d345d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/> as a decimal.<\/p>\n<\/div>\n<div id=\"fs-id1170655124919\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1170655124777\">Since a fraction bar means division, we begin by writing <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-44cf49c06a351926440bb2ad833776c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-241628c682fc3b6f65f2194a73523287_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"25\" style=\"vertical-align: -5px;\" \/>. Now divide.<\/p>\n<p><span id=\"fs-id1170654966693\" data-type=\"media\" data-alt=\"This is a long division problem with 8 dividing 5.000 and 0.625 as the quotient. Below 5.000 we have 48, a solid horizontal line, 20, 16, a solid horizontal line, 40, 40, and a final horizontal line. So five eighths equals 0.625.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_017_img_new.jpg\" alt=\"This is a long division problem with 8 dividing 5.000 and 0.625 as the quotient. Below 5.000 we have 48, a solid horizontal line, 20, 16, a solid horizontal line, 40, 40, and a final horizontal line. So five eighths equals 0.625.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655024912\" data-type=\"problem\">\n<p id=\"fs-id1170655229974\">Write <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9dbe942ff30fccbe3cafef9973811e06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/> as a decimal.<\/p>\n<\/div>\n<div id=\"fs-id1170655154221\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655129731\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d079f44bac785047ece87b816dc283c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#48;&#46;&#56;&#55;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"53\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p>When we divide, we will not always get a zero remainder. Sometimes the quotient ends up with a decimal that repeats. A repeating decimal is a decimal in which the last digit or group of digits repeats endlessly. A bar is placed over the repeating block of digits to indicate it repeats.<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-id1170655219747\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Repeating Decimal<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>A <strong data-effect=\"bold\">repeating decimal<\/strong> is a decimal in which the last digit or group of digits repeats endlessly.<\/p>\n<\/div>\n<\/div>\n<p>A bar is placed over the repeating block of digits to indicate it repeats.<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654919361\" data-type=\"problem\">\n<p id=\"fs-id1170654924199\">Write <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9e23bf4c5b143d6c6932ef52cae9b526_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#51;&#125;&#123;&#50;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/> as a decimal.<\/p>\n<\/div>\n<div id=\"fs-id1170655025946\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<\/div>\n<div data-type=\"title\"><\/div>\n<div id=\"fs-id1170655025946\" data-type=\"solution\">\n<p><span id=\"fs-id1170654982890\" data-type=\"media\" data-alt=\"The number 43\/22 is given. The direction is given to \u201cDivide 43 by 22.\u201d A long division problem is given with 22 dividing 43.00000 with 1.95454 as the quotient. Below 43.00000 we have 22, a solid horizontal line, 210, 198, a solid horizontal line, 120, 110, a horizontal line, 100, 88, a solid horizontal line, 120, 110, a solid horizontal line, 100, 88, a solid horizontal line, and then three dots. It is noted that the 120 repeats and that the 100 repeats. This is further explicated as \u201cThe pattern repeats, so the numbers in the quotient will repeat as well. At the end, we are given the statement that 43\/22 equals 1.954 with a small horizontal line over the 54.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_018_img_new.jpg\" alt=\"The number 43\/22 is given. The direction is given to \u201cDivide 43 by 22.\u201d A long division problem is given with 22 dividing 43.00000 with 1.95454 as the quotient. Below 43.00000 we have 22, a solid horizontal line, 210, 198, a solid horizontal line, 120, 110, a horizontal line, 100, 88, a solid horizontal line, 120, 110, a solid horizontal line, 100, 88, a solid horizontal line, and then three dots. It is noted that the 120 repeats and that the 100 repeats. This is further explicated as \u201cThe pattern repeats, so the numbers in the quotient will repeat as well. At the end, we are given the statement that 43\/22 equals 1.954 with a small horizontal line over the 54.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655154772\" data-type=\"problem\">\n<p id=\"fs-id1170655125921\">Write <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a69120f943b30d7d2cc5e3c32b5ffde0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#55;&#125;&#123;&#49;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"14\" style=\"vertical-align: -7px;\" \/> as a decimal.<\/p>\n<\/div>\n<div id=\"fs-id1170655163739\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655166549\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-09ccfc66a3cb6efbb1630dcc9cf395ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#46;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#8212;&#125;&#125;&#123;&#52;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"36\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170654958830\">Sometimes we may have to simplify expressions with fractions and decimals together.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655154796\" data-type=\"problem\">\n<p id=\"fs-id1170655089358\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b5a38cc8a5b9802edd4977b91acc6229_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#56;&#125;&#43;&#54;&#46;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"53\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654929183\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1170655026448\">First we must change one number so both numbers are in the same form. We can change the fraction to a decimal, or change the decimal to a fraction. Usually it is easier to change the fraction to a decimal.<\/p>\n<table id=\"eip-id1169754088588\" style=\"width: 100%;\" summary=\"The expression 7\/8 plus 6.4 is given. The direction is given to \u201cChange 7\/8 to a decimal.\u201d To the right of this we have the long division problem with 8 dividing 7.000 and 0.875 as the quotient. Below 7.000 we have 64, a solid horizontal line, 60, 56, a solid horizontal line, 40, 40, a final horizontal line, and 0. The next direction is to \u201cAdd.\u201d To the right of this we have 0.875 + 6.4, so seven eighths plus 6.4 equals 7.275.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b5a38cc8a5b9802edd4977b91acc6229_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#56;&#125;&#43;&#54;&#46;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"53\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Change <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-27a06edc5fe1932bd0c3274d9af93920_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> to a decimal.<\/td>\n<td><span id=\"eip-id1169749852706\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_ElemAlg_Figure_01_07_019_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c4c248a79b023a1b4090d18c3ce69f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#56;&#55;&#53;&#43;&#54;&#46;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"85\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9f6c181a608f85ef32eb6a995196e397_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#46;&#50;&#55;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"40\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td>So, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-bfdb5773a1b6ecfea3d55f91f0bef54e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#56;&#125;&#43;&#54;&#46;&#52;&#61;&#55;&#46;&#50;&#55;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"117\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655229698\" data-type=\"problem\">\n<p id=\"fs-id1170654953761\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-80352932955c1bf0685f57fae0b9df68_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#56;&#125;&#43;&#52;&#46;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"53\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654984861\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654928209\">5.275<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Key Concepts<\/h1>\n<ul id=\"fs-id1170655106869\" data-bullet-style=\"bullet\">\n<li><strong data-effect=\"bold\">Round a Decimal<\/strong>\n<ol id=\"fs-id1170655114584\" class=\"stepwise\" type=\"1\">\n<li>Locate the given place value and mark it with an arrow.<\/li>\n<li>Underline the digit to the right of the place value.<\/li>\n<li>Is this digit greater than or equal to 5? Yes\u2014add 1 to the digit in the given place value. No\u2014do <u data-effect=\"underline\">not<\/u> change the digit in the given place value.<\/li>\n<li>Rewrite the number, deleting all digits to the right of the rounding digit.<\/li>\n<\/ol>\n<\/li>\n<li><strong data-effect=\"bold\">Add or Subtract Decimals<\/strong>\n<ol id=\"fs-id1170655063011\" class=\"stepwise\" type=\"1\">\n<li>Write the numbers so the decimal points line up vertically.<\/li>\n<li>Use zeros as place holders, as needed.<\/li>\n<li>Add or subtract the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers.<\/li>\n<\/ol>\n<\/li>\n<li><strong data-effect=\"bold\">Multiply Decimals<\/strong>\n<ol id=\"fs-id1170655162096\" class=\"stepwise\" type=\"1\">\n<li>Determine the sign of the product.<\/li>\n<li>Write in vertical format, lining up the numbers on the right. Multiply the numbers as if they were whole numbers, temporarily ignoring the decimal points.<\/li>\n<li>Place the decimal point. The number of decimal places in the product is the sum of the decimal places in the factors.<\/li>\n<li>Write the product with the appropriate sign.<\/li>\n<\/ol>\n<\/li>\n<li><strong data-effect=\"bold\">Multiply a Decimal by a Power of Ten<\/strong>\n<ol id=\"fs-id1170655037577\" class=\"stepwise\" type=\"1\">\n<li>Move the decimal point to the right the same number of places as the number of zeros in the power of 10.<\/li>\n<li>Add zeros at the end of the number as needed.<\/li>\n<\/ol>\n<\/li>\n<li><strong data-effect=\"bold\">Divide Decimals<\/strong>\n<ol id=\"fs-id1170655201026\" class=\"stepwise\" type=\"1\">\n<li>Determine the sign of the quotient.<\/li>\n<li>Make the divisor a whole number by \u201cmoving\u201d the decimal point all the way to the right. \u201cMove\u201d the decimal point in the dividend the same number of places &#8211; adding zeros as needed.<\/li>\n<li>Divide. Place the decimal point in the quotient above the decimal point in the dividend.<\/li>\n<li>Write the quotient with the appropriate sign.<\/li>\n<\/ol>\n<\/li>\n<li><strong data-effect=\"bold\">Convert a Decimal to a Proper Fraction<\/strong>\n<ol id=\"fs-id1170654983497\" class=\"stepwise\" type=\"1\">\n<li>Determine the place value of the final digit.<\/li>\n<li>Write the fraction: numerator\u2014the \u2018numbers\u2019 to the right of the decimal point; denominator\u2014the place value corresponding to the final digit.<\/li>\n<\/ol>\n<\/li>\n<li><strong data-effect=\"bold\">Convert a Fraction to a Decimal<\/strong> Divide the numerator of the fraction by the denominator.<\/li>\n<\/ul>\n<h1>1.4 Exercise Set<\/h1>\n<p id=\"fs-id1166422830559\">In the following exercises, round each number to the nearest tenth.<\/p>\n<ol class=\"twocolumn\">\n<li>0.67<\/li>\n<li>2.84<\/li>\n<\/ol>\n<p id=\"fs-id1170655041277\">In the following exercises, round each number to the nearest hundredth.<\/p>\n<ol class=\"twocolumn\" start=\"3\">\n<li>0.845<\/li>\n<li>0.299<\/li>\n<li>4.098<\/li>\n<\/ol>\n<div id=\"fs-id1170655041281\" data-type=\"exercise\">\n<div id=\"fs-id1170654965811\" data-type=\"problem\">In the following exercises, round each number to the nearest a) hundredth b) tenth c) whole number.<\/div>\n<ol class=\"twocolumn\" start=\"6\">\n<li data-type=\"problem\">5.781<\/li>\n<li data-type=\"problem\">63.479<\/li>\n<\/ol>\n<\/div>\n<p id=\"fs-id1166422576116\">In the following exercises, add or subtract.<\/p>\n<ol class=\"twocolumn\" start=\"8\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1c90e9a49d49b5f53261b5161c543931_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;&#46;&#57;&#50;&#43;&#55;&#46;&#53;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"93\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8224174caf461926d5c9d90b7cf4fd76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#49;&#46;&#55;&#54;&#45;&#51;&#48;&#46;&#57;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"103\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-fc56dae7896fffb50553b1752c74ad9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#54;&#46;&#53;&#51;&#45;&#50;&#52;&#46;&#51;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"116\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8b667f13c951d748d4441ed01c01ab17_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#56;&#46;&#54;&#57;&#43;&#51;&#49;&#46;&#52;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"116\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9446c4d52ab3e0238d118948713366ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#50;&#46;&#53;&#45;&#49;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"80\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b5a876140d9276feec379a3410be9710_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#43;&#48;&#46;&#55;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"70\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6d7e4e07ad64a7668557c26af23478be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#49;&#46;&#57;&#53;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#48;&#46;&#52;&#54;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"139\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-04329a849fd13da72e55d368855df813_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#53;&#46;&#48;&#49;&#45;&#51;&#46;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"85\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2ebd7337a99ff13161d28ddc0c6418ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#46;&#53;&#49;&#45;&#55;&#46;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"76\" style=\"vertical-align: -1px;\" \/><\/li>\n<\/ol>\n<p id=\"fs-id1166420388478\">In the following exercises, multiply.<\/p>\n<ol class=\"twocolumn\" start=\"17\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4fde3c67c097e8ad34fa8a32318318c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#46;&#50;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#46;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-65c8260dc026b600dafff3a0583974c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#46;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#46;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4a78b15ad68565111112045456261fb0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#46;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#46;&#55;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"97\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-20721ef49950b8a59f7ee1a2908e9edc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#46;&#49;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#53;&#46;&#50;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"129\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0be1395202e50fdf220fd5823d8fb02e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#46;&#48;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#49;&#46;&#55;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"101\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-27ac039f6cc1c41adbac82ac99f94c0e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#46;&#50;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"78\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d0d251ec8ec732db09c90b7f1d9418a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#53;&#46;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#48;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"96\" style=\"vertical-align: -4px;\" \/><\/li>\n<\/ol>\n<div id=\"fs-id1170655084877\" data-type=\"exercise\">\n<div id=\"fs-id1170654983718\" data-type=\"problem\">In the following exercises, divide.<\/div>\n<ol class=\"twocolumn\" start=\"24\">\n<li data-type=\"problem\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f366bb89c40bdc6ad113b6cd4eb5a005_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#46;&#55;&#53;&#92;&#100;&#105;&#118;&#32;&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"70\" style=\"vertical-align: -1px;\" \/><\/li>\n<li data-type=\"problem\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-672f237508e906a1a80f5da6b0a6dfa6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#36;&#49;&#49;&#55;&#46;&#50;&#53;&#92;&#100;&#105;&#118;&#32;&#52;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"98\" style=\"vertical-align: -1px;\" \/><\/li>\n<li data-type=\"problem\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-30bb79a388613a0eba501ba6c1426248_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#54;&#92;&#100;&#105;&#118;&#32;&#48;&#46;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"66\" style=\"vertical-align: -1px;\" \/><\/li>\n<li data-type=\"problem\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-86b5222043f8c79e778ffbc3e3f29575_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#52;&#52;&#92;&#100;&#105;&#118;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#48;&#46;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"102\" style=\"vertical-align: -5px;\" \/><\/li>\n<li data-type=\"problem\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6658a6e92fce2d7c474025154227310c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#46;&#55;&#53;&#92;&#100;&#105;&#118;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#48;&#46;&#48;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"125\" style=\"vertical-align: -5px;\" \/><\/li>\n<li data-type=\"problem\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9c72b6d65fad8b7aa6fff5340371949d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#46;&#50;&#92;&#100;&#105;&#118;&#32;&#50;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"66\" style=\"vertical-align: -1px;\" \/><\/li>\n<li data-type=\"problem\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a3ad94d7161047a549e138cd7d0e4bec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;&#92;&#100;&#105;&#118;&#32;&#48;&#46;&#53;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"69\" style=\"vertical-align: -1px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1170655228709\" data-type=\"exercise\">\n<h2><span style=\"font-weight: normal; text-align: initial; font-family: 'Times New Roman', Georgia, 'SBL Greek', serif; font-size: 14pt;\">In the following exercises, write each decimal as a fraction.<\/span><\/h2>\n<ol class=\"twocolumn\" start=\"31\">\n<li>0.04<\/li>\n<li>0.52<\/li>\n<li>1.25<\/li>\n<li>0.375<\/li>\n<li>0.095<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1170655113928\" data-type=\"exercise\">\n<div id=\"fs-id1170655113931\" data-type=\"problem\">In the following exercises, convert each fraction to a decimal.<\/div>\n<ol class=\"twocolumn\" start=\"36\">\n<li data-type=\"problem\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-dec0bfaac7a24643c8e5fb816c534b44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#55;&#125;&#123;&#50;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/li>\n<li data-type=\"problem\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5b68294c2a73f2ea0d02861b81ab877d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#49;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/li>\n<li data-type=\"problem\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9e72d7a0997365dfea5572a0c23639b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#49;&#48;&#125;&#123;&#50;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"39\" style=\"vertical-align: -6px;\" \/><\/li>\n<li data-type=\"problem\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ebcdbcc51438bada11c32ca6579971cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#53;&#125;&#123;&#49;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"14\" style=\"vertical-align: -7px;\" \/><\/li>\n<li data-type=\"problem\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b36bd9a81e0ab3812394c658cc893c8e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#53;&#125;&#123;&#49;&#49;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"21\" style=\"vertical-align: -7px;\" \/><\/li>\n<li data-type=\"problem\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-32a990e4f1a9e30cffbf428d9f3e1a58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#46;&#52;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"53\" style=\"vertical-align: -6px;\" \/><\/li>\n<\/ol>\n<ol start=\"42\">\n<li><strong data-effect=\"bold\">Salary Increase.<\/strong> Marta got a raise and now makes &#36;58,965.95 a year. Round this number to the nearest<br \/>\na) dollar<br \/>\nb) thousand dollars<br \/>\nc) ten thousand dollars.<\/li>\n<li><strong data-effect=\"bold\">Sales Tax.<\/strong> Hyo Jin lives in Vancouver. She bought a refrigerator for &#36;1,624.99 and when the clerk calculated the sales tax it came out to exactly &#36;142.186625. Round the sales tax to the nearest<br \/>\na) penny and<br \/>\nb) dollar.<\/li>\n<li><strong data-effect=\"bold\">Paycheck.<\/strong> Annie has two jobs. She gets paid &#36;14.04 per hour for tutoring at Community College and &#36;8.75 per hour at a coffee shop. Last week she tutored for 8 hours and worked at the coffee shop for 15 hours.<br \/>\na) How much did she earn?<br \/>\nb) If she had worked all 23 hours as a tutor instead of working both jobs, how much more would she have earned?<\/li>\n<\/ol>\n<\/div>\n<p><span style=\"font-family: Helvetica, Arial, 'GFS Neohellenic', sans-serif; font-size: 1.2em; font-weight: bold;\">Glossary<\/span><\/p>\n<div class=\"textbox shaded\" data-type=\"glossary\">\n<dl id=\"fs-id1166425139638\">\n<dt>decimal<\/dt>\n<dd id=\"fs-id1166424911849\">A decimal is another way of writing a fraction whose denominator is a power of ten.<\/dd>\n<\/dl>\n<dl id=\"fs-id1166425061744\">\n<dt>repeating decimal<\/dt>\n<dd id=\"fs-id1166425061749\">A repeating decimal is a decimal in which the last digit or group of digits repeats endlessly.<\/dd>\n<\/dl>\n<\/div>\n<h1>Answers:<\/h1>\n<ol class=\"twocolumn\">\n<li>0.7<\/li>\n<li>2.8<\/li>\n<li>0.85<\/li>\n<li>0.30<\/li>\n<li>4.10<\/li>\n<li>a) 5.78 b) 5.8 c) 6<\/li>\n<li>a) 63.48 b) 63.5 c) 63<\/li>\n<li>24.48<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-deed6f942143150a53b92cc16a8627ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;&#46;&#50;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"45\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-393972d398a9ba2e7a4b7370eadfbcb9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#48;&#46;&#57;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"53\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8fdfa2b092f8324f50610d7e9d34726d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;&#46;&#50;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"44\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b950529f706a9a7e0ba550d56bfaab44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#55;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"44\" style=\"vertical-align: 0px;\" \/><\/li>\n<li>15.73<\/li>\n<li>102.212<\/li>\n<li>51.31<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-cadc76228d39486be78625fcc9adc6c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#46;&#56;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"45\" style=\"vertical-align: -1px;\" \/><\/li>\n<li>0.144<\/li>\n<li>42.008<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b02d2500eeec3c4c7683d4665c8b797c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#49;&#46;&#54;&#53;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"63\" style=\"vertical-align: -1px;\" \/><\/li>\n<li>337.8914<\/li>\n<li>1.305<\/li>\n<li>92.4<\/li>\n<li>55,200<\/li>\n<li>0.19<\/li>\n<li>&#36;2.44<\/li>\n<li>3<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b2c89e7492512d2df59c5e900b950453_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#46;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"36\" style=\"vertical-align: -1px;\" \/><\/li>\n<li>35<\/li>\n<li>2.08<\/li>\n<li>20<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-987c8c247ee1bfbcaa09ef7b7ce42fbb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0ca4e2ec921f920b0006a9746c72ead6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#51;&#125;&#123;&#50;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-27f26f48f049d16d7bf76d51e1f91cef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a50f9f96c608e65c404d41e0ef6f8a47_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-597bcb3c2f10c32b9c574b0e300dfb5d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#57;&#125;&#123;&#50;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"21\" style=\"vertical-align: -6px;\" \/><\/li>\n<li>0.85<\/li>\n<li>2.75<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-01027fb3f026eb695283721aac4e9e8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#50;&#46;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"45\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b83a3a06dd8f60750ff86f6cbbc324ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#8212;&#125;&#125;&#123;&#51;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"36\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8cf25a13d3c306486559f15d4702a285_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#8212;&#125;&#125;&#123;&#49;&#51;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"45\" style=\"vertical-align: -1px;\" \/><\/li>\n<li>3.025<\/li>\n<li>a) &#36;58,966 b) &#36;59,000 c) &#36;60,000<\/li>\n<li>a) &#36;142.19; b) &#36;142<\/li>\n<li>a) &#36;243.57 b) &#36;79.35<\/li>\n<\/ol>\n<h1>Attributions<\/h1>\n<p>This chapter has been adapted from \u201cDecimals\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/elementary-algebra\"><em>Elementary Algebra<\/em><\/a> (OpenStax) by Lynn Marecek and MaryAnne Anthony-Smith, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.<\/p>\n","protected":false},"author":125,"menu_order":4,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-172","chapter","type-chapter","status-publish","hentry"],"part":21,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/172","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/users\/125"}],"version-history":[{"count":5,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/172\/revisions"}],"predecessor-version":[{"id":2156,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/172\/revisions\/2156"}],"part":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/parts\/21"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/172\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/media?parent=172"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapter-type?post=172"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/contributor?post=172"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/license?post=172"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}