{"id":47,"date":"2022-06-20T13:21:36","date_gmt":"2022-06-20T17:21:36","guid":{"rendered":"https:\/\/opentextbc.ca\/nursingnumeracy\/chapter\/scientific-notation\/"},"modified":"2023-06-28T13:01:55","modified_gmt":"2023-06-28T17:01:55","slug":"scientific-notation","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/nursingnumeracy\/chapter\/scientific-notation\/","title":{"raw":"Scientific Notation","rendered":"Scientific Notation"},"content":{"raw":"<h1>Lesson<\/h1>\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Outcomes<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nBy the end of this chapter, learners will be able to\n<ul>\n \t<li>explain the use of exponents,<\/li>\n \t<li>describe the system of scientific notation, and<\/li>\n \t<li>convert numbers from scientific form to standard form.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h2>Exponents<\/h2>\nYou will see exponents being used in various ways related to health care topics. For instance, it might be for very large, or very small, amounts of medication or diagnostic test values. You may also come across exponents when reading statistical information in journal articles.\n\nExponents are numbers written in superscript, to the right of a number, called the base. Exponents can be positive or negative. A positive exponent is used to identify how may times the base number should be multiplied by itself. This number is referred to as the power. A negative exponent is the reciprocal of the number with a positive exponent. In general, positive exponents are related to large numbers while negative exponents are related to small numbers. While it is unlikely you will need to calculate what the power of a number equals, the following practice questions may help you to gain an appreciation for how the values of numbers change in size depending on the size of the base number and the size of the exponent.\n<div class=\"textbox\">\n<p style=\"text-align: center;\">Positive Exponent<\/p>\nBase<sup>Exponent<\/sup>\n\nFor example: [latex]2^{6}[\/latex] or [latex]2\\times{2}\\times{2}\\times{2}\\times{2}\\times{2}=64[\/latex]\n\nThis can be read aloud as \"two to the sixth power.\"\n\n<\/div>\n<div class=\"textbox\">\n<p style=\"text-align: center;\">Negative Exponent<\/p>\n[latex]\\begin{align*}\n2^{\u22126}&amp;=\\dfrac{1}{2^6} \\\\ \\\\\n&amp;= \\dfrac{1}{2\\times2\\times2\\times2\\times2\\times2} \\\\ \\\\\n&amp;=\\dfrac{1}{64} \\\\ \\\\\n&amp;=0.015625\n\\end{align*}[\/latex]\n\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Sample Exercise 5.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<ol>\n \t<li>Write five to the power of three.<\/li>\n \t<li>What does five to the power of three equal?<\/li>\n<\/ol>\n<details><summary><strong>Answers:<\/strong><\/summary>\n<ol>\n \t<li>[latex]5^{3}[\/latex]<\/li>\n \t<li>[latex]5\\times{5}\\times{5}=125[\/latex]<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Sample Exercise 5.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nWhat number is represented by [latex]6^{-4}[\/latex]?\n\n<details open=\"open\"><summary><strong>Answers:<\/strong><\/summary>[latex]\\begin{align*}\n6^{\u22124}&amp;=\\dfrac{1}{6^4} \\\\ \\\\\n&amp;=\\dfrac{1}{1296} \\\\ \\\\\n&amp;=0.0007716049382716\n\\end{align*}[\/latex]\n\n<\/details><\/div>\n<\/div>\n<h2>Scientific Notation<\/h2>\nScientific notation is a special way of concisely expressing very large and very small numbers. You can think of it like an abbreviation of a number. When a number is not abbreviated, it is known as a number in standard form. When numbers are written in scientific notation, the base number is multiplied or divided by a power of 10 to make the number large or small. When the exponent is positive, the base number is multiplied by 10, a number of times equal to the number of the exponent. When the exponent is negative, the base number is divided by 10, a number of times equal to the number of the exponent.\n<div class=\"textbox\">\n<p style=\"text-align: center;\">Positive Exponents<\/p>\nnumber x 10<sup>n<\/sup>\n\n[latex]\\begin{align*}\n\\text{a. }{3.4\\times 10^{5}}&amp;={3.4\\times10\\times10\\times10\\times10\\times10} \\\\ \\\\\n&amp;=340000\\end{align*}[\/latex]\n\n[latex]\\begin{align*}\n\\text{b. }{2.7\\times 10^{3}}&amp;={2.7\\times10\\times10\\times10} \\\\ \\\\\n&amp;=2700\\end{align*}[\/latex]\n\n[latex]\\begin{align*}\n\\text{c. }{7.1\\times 10^{8}}&amp;={7.1\\times10\\times10\\times10\\times10\\times10\\times10\\times10\\times10} \\\\ \\\\\n&amp;=710000000\\end{align*}[\/latex]\n\n<\/div>\n<div class=\"textbox\">\n<p style=\"text-align: center;\">Negative Exponents<\/p>\nnumber \u00d7 10\u2212<sup>n<\/sup>\n\n[latex]\\begin{align*}\n\\text{a. }{4.2\\times 10^{\u22123}}&amp;=4.2\\times\\dfrac{1}{10^{3}} \\\\ \\\\\n&amp;=4.2\\times \\dfrac{1}{10\\times 10\\times 10} \\\\ \\\\\\\n&amp;=\\dfrac{4.2}{1000} \\\\ \\\\\n&amp;=0.0042\\end{align*}[\/latex]\n\n[latex]\\begin{align*}\n\\text{b. }{9.3\\times10^{\u22125}}&amp;=9.3\\times\\dfrac{1}{10^{5}} \\\\ \\\\\n&amp;=9.3\\times\\dfrac{1}{10\\times10\\times10\\times10\\times10} \\\\ \\\\\n&amp;=\\dfrac{9.3}{10\\times10\\times10\\times10\\times10} \\\\ \\\\\n&amp;=\\dfrac{9.3}{10000} \\\\ \\\\\n&amp;=0.00093\\end{align*}[\/latex]\n\nHere you can see in scientific notation, the number is divided by 10 the same number of times as the number of the exponent.\n\n<\/div>\nWhen determining what the number is which is represented by scientific notation, you can easily do this just by moving the decimal place over by the number of spaces equal to the exponent. The decimal place will move to the right with positive exponents, making the number larger, and to the left for negative exponents, making the number smaller.\n<div class=\"textbox\">\n<p style=\"text-align: center;\">Positive Exponents<\/p>\nMove the decimal to the right to make the number larger.\nIn this example, the exponent, or the power, is 5. Move the decimal five places to the right. (The numbers in subscript show the number of places the decimal is moving.)\n<p style=\"text-align: center;\">eg. [latex]3.4\\times{10}^{5}[\/latex]\u00a0 = 3.4 <sub style=\"text-align: initial; background-color: initial;\">1<\/sub><span style=\"text-align: initial; background-color: initial; font-size: 1em;\"> 0 <\/span><sub style=\"text-align: initial; background-color: initial;\">2<\/sub><span style=\"text-align: initial; background-color: initial; font-size: 1em;\"> 0 <\/span><sub style=\"text-align: initial; background-color: initial;\">3<\/sub><span style=\"text-align: initial; background-color: initial; font-size: 1em;\"> 0 <\/span><sub style=\"text-align: initial; background-color: initial;\">4<\/sub><span style=\"text-align: initial; background-color: initial; font-size: 1em;\"> 0 <\/span><sub style=\"text-align: initial; background-color: initial;\">5 <\/sub><span style=\"text-align: initial; background-color: initial; font-size: 1em;\">= 340000<\/span><\/p>\n\n<\/div>\n<div class=\"textbox\">\n<p style=\"text-align: center;\">Negative Exponents<\/p>\nMove the decimal to the left to make the number smaller.\nIn this example, the exponent, or the power, is 3. Move the decimal three places to the right.\n<p style=\"text-align: center;\">eg. [latex]4.2\\times{10}^{-3}[\/latex] =\u00a0 <sub>3<\/sub> 0\u00a0<sub>2<\/sub> 0\u00a0<sub>1<\/sub> 4 . 2\u00a0 = 0.0042<\/p>\n\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Sample Exercise 5.3<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nWrite [latex]1.7\\times{10^{6}}[\/latex]<sup style=\"text-align: initial;\">\u00a0<\/sup><span style=\"text-align: initial; font-size: 1em;\">in standard form.<\/span>\n\n<details open=\"open\"><summary><strong>Answers:<\/strong><\/summary>[latex]1700000[\/latex]\n\nMove the decimal to the right six places. ([latex]1.7\\times{10^{6}}[\/latex]\u00a0 = 1.7 <sub>1<\/sub> 0 <sub>2<\/sub> 0 <sub>3<\/sub> 0 <sub>4<\/sub> 0 <sub>5 <\/sub>0 <sub>6<\/sub>= [latex]1700000[\/latex])\n\n<\/details><\/div>\n<\/div>\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Key Takeaways<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<ul>\n \t<li>Exponents are helpful when writing very large and very small numbers.<\/li>\n \t<li>Numbers with positive exponents will be greater or equal to one.<\/li>\n \t<li>Numbers with negative exponents will be less than one.<\/li>\n \t<li>When determining the value of a number written in scientific notation, if the power of 10 is positive you move the decimal to the right.<\/li>\n \t<li>When determining the value of a number written in scientific notation, if the power of 10 is negative you move the decimal to the left.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1>Practice Set 5.1: Determining the numerical value of numbers with positive exponents<\/h1>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Practice Set 5.1: Determining the numerical value of numbers with positive exponents<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nCalculate the value of the following numbers with exponents:\n<ol class=\"twocolumn\">\n \t<li>[latex]5^{4}[\/latex]<\/li>\n \t<li>[latex]2^{7}[\/latex]<\/li>\n \t<li>[latex]4^{2}[\/latex]<\/li>\n \t<li>[latex]8^{3}[\/latex]<\/li>\n \t<li>[latex]6^{6}[\/latex]<\/li>\n \t<li>[latex]12^{4}[\/latex]<\/li>\n \t<li>[latex]3^{15}[\/latex]<\/li>\n \t<li>[latex]9^{5}[\/latex]<\/li>\n \t<li>[latex]10^{3}[\/latex]<\/li>\n \t<li>[latex]3^{8}[\/latex]<\/li>\n<\/ol>\n<details><summary><strong>Answers:<\/strong><\/summary>\n<ol class=\"twocolumn\">\n \t<li>[latex]625[\/latex]<\/li>\n \t<li>[latex]128[\/latex]<\/li>\n \t<li>[latex]16[\/latex]<\/li>\n \t<li>[latex]512[\/latex]<\/li>\n \t<li>[latex]46656[\/latex]<\/li>\n \t<li>[latex]20736[\/latex]<\/li>\n \t<li>[latex]14348907[\/latex]<\/li>\n \t<li>[latex]59049[\/latex]<\/li>\n \t<li>[latex]1000[\/latex]<\/li>\n \t<li>[latex]6561[\/latex]<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<h1>Practice Set 5.2: Determining the numerical value of numbers with negative exponents<\/h1>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Practice Set 5.2: Determining the numerical value of numbers with negative exponents<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nCalculate the value of the following numbers with exponents:\n<ol class=\"twocolumn\">\n \t<li>[latex]2^{-4}[\/latex]<\/li>\n \t<li>[latex]10^{-2}[\/latex]<\/li>\n \t<li>[latex]4^{-3}[\/latex]<\/li>\n \t<li>[latex]7^{-4}[\/latex]<\/li>\n \t<li>[latex]32^{-1}[\/latex]<\/li>\n \t<li>[latex]5^{-5}[\/latex]<\/li>\n \t<li>[latex]3^{-5}[\/latex]<\/li>\n \t<li>[latex]7^{-3}[\/latex]<\/li>\n \t<li>[latex]8^{-2}[\/latex]<\/li>\n \t<li>[latex]3.3^{-4}[\/latex]<\/li>\n<\/ol>\n<details><summary><strong>Answers:<\/strong><\/summary>\n<ol class=\"twocolumn\">\n \t<li>[latex]0.0625[\/latex]<\/li>\n \t<li>[latex]0.01[\/latex]<\/li>\n \t<li>[latex]0.015625[\/latex]<\/li>\n \t<li>[latex]0.00041649312786339[\/latex]<\/li>\n \t<li>[latex]0.03125[\/latex]<\/li>\n \t<li>[latex]0.00032[\/latex]<\/li>\n \t<li>[latex]0.0041152263374486[\/latex]<\/li>\n \t<li><span id=\"MathJax-Span-52\" class=\"mrow\"><span id=\"MathJax-Span-54\" class=\"mn\">[latex]0.0029154518950437[\/latex]<\/span><\/span><\/li>\n \t<li>[latex]0.015625[\/latex]<\/li>\n \t<li><span id=\"MathJax-Span-33\" class=\"mrow\"><span id=\"MathJax-Span-35\" class=\"mn\">[latex]0.0084322648810503[\/latex]<\/span><\/span><\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<h1>Practice Set 5.3: Determining the value of numbers written in scientific notation<\/h1>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Practice Set 5.3: Determining the value of numbers written in scientific notation<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nConvert each number to standard form.\n<ol class=\"twocolumn\">\n \t<li>[latex]2.8\\times{10^{4}}[\/latex]<\/li>\n \t<li>[latex]7.34\\times{10^{-6}}[\/latex]<\/li>\n \t<li>[latex]4.9\\times{10^{7}}[\/latex]<\/li>\n \t<li>[latex]5.2\\times{10^{3}}[\/latex]<\/li>\n \t<li>[latex]1.54\\times{10^{-4}}[\/latex]<\/li>\n \t<li>[latex]6.241\\times{10^{-8}}[\/latex]<\/li>\n \t<li>[latex]5.9\\times{10^{5}}[\/latex]<\/li>\n \t<li>[latex]3.278\\times{10^{-5}}[\/latex]<\/li>\n \t<li>[latex]4.4\\times{10^{2}}[\/latex]<\/li>\n \t<li>[latex]8.623\\times{10^{6}}[\/latex]<\/li>\n<\/ol>\n<details><summary><strong>Answers:<\/strong><\/summary>\n<ol class=\"twocolumn\">\n \t<li>[latex]28000[\/latex]<\/li>\n \t<li>[latex]0.00000734[\/latex]<\/li>\n \t<li>[latex]49000000[\/latex]<\/li>\n \t<li>[latex]5200[\/latex]<\/li>\n \t<li>[latex]0.000154[\/latex]<\/li>\n \t<li>[latex]0.00000006241[\/latex]<\/li>\n \t<li>[latex]590000[\/latex]<\/li>\n \t<li>[latex]0.0000327[\/latex]<\/li>\n \t<li>[latex]440[\/latex]<\/li>\n \t<li>[latex]8623000[\/latex]<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<div class=\"textbox shaded\">This chapter is adapted from Unit 11: Exponents, Roots and Scientific Notation in the book <a href=\"https:\/\/collection.bccampus.ca\/textbooks\/key-concepts-of-intermediate-level-math-bccampus-204\/\"><em>Key Concepts of Intermediate Level Math<\/em><\/a> by Meizhong Wang, licensed as <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0<\/a>.<\/div>","rendered":"<h1>Lesson<\/h1>\n<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Outcomes<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>By the end of this chapter, learners will be able to<\/p>\n<ul>\n<li>explain the use of exponents,<\/li>\n<li>describe the system of scientific notation, and<\/li>\n<li>convert numbers from scientific form to standard form.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h2>Exponents<\/h2>\n<p>You will see exponents being used in various ways related to health care topics. For instance, it might be for very large, or very small, amounts of medication or diagnostic test values. You may also come across exponents when reading statistical information in journal articles.<\/p>\n<p>Exponents are numbers written in superscript, to the right of a number, called the base. Exponents can be positive or negative. A positive exponent is used to identify how may times the base number should be multiplied by itself. This number is referred to as the power. A negative exponent is the reciprocal of the number with a positive exponent. In general, positive exponents are related to large numbers while negative exponents are related to small numbers. While it is unlikely you will need to calculate what the power of a number equals, the following practice questions may help you to gain an appreciation for how the values of numbers change in size depending on the size of the base number and the size of the exponent.<\/p>\n<div class=\"textbox\">\n<p style=\"text-align: center;\">Positive Exponent<\/p>\n<p>Base<sup>Exponent<\/sup><\/p>\n<p>For example: [latex]2^{6}[\/latex] or [latex]2\\times{2}\\times{2}\\times{2}\\times{2}\\times{2}=64[\/latex]<\/p>\n<p>This can be read aloud as &#8220;two to the sixth power.&#8221;<\/p>\n<\/div>\n<div class=\"textbox\">\n<p style=\"text-align: center;\">Negative Exponent<\/p>\n<p>[latex]\\begin{align*} 2^{\u22126}&=\\dfrac{1}{2^6} \\\\ \\\\ &= \\dfrac{1}{2\\times2\\times2\\times2\\times2\\times2} \\\\ \\\\ &=\\dfrac{1}{64} \\\\ \\\\ &=0.015625 \\end{align*}[\/latex]<\/p>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Sample Exercise 5.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol>\n<li>Write five to the power of three.<\/li>\n<li>What does five to the power of three equal?<\/li>\n<\/ol>\n<details>\n<summary><strong>Answers:<\/strong><\/summary>\n<ol>\n<li>[latex]5^{3}[\/latex]<\/li>\n<li>[latex]5\\times{5}\\times{5}=125[\/latex]<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Sample Exercise 5.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>What number is represented by [latex]6^{-4}[\/latex]?<\/p>\n<details open=\"open\">\n<summary><strong>Answers:<\/strong><\/summary>\n<p>[latex]\\begin{align*} 6^{\u22124}&=\\dfrac{1}{6^4} \\\\ \\\\ &=\\dfrac{1}{1296} \\\\ \\\\ &=0.0007716049382716 \\end{align*}[\/latex]<\/p>\n<\/details>\n<\/div>\n<\/div>\n<h2>Scientific Notation<\/h2>\n<p>Scientific notation is a special way of concisely expressing very large and very small numbers. You can think of it like an abbreviation of a number. When a number is not abbreviated, it is known as a number in standard form. When numbers are written in scientific notation, the base number is multiplied or divided by a power of 10 to make the number large or small. When the exponent is positive, the base number is multiplied by 10, a number of times equal to the number of the exponent. When the exponent is negative, the base number is divided by 10, a number of times equal to the number of the exponent.<\/p>\n<div class=\"textbox\">\n<p style=\"text-align: center;\">Positive Exponents<\/p>\n<p>number x 10<sup>n<\/sup><\/p>\n<p>[latex]\\begin{align*} \\text{a. }{3.4\\times 10^{5}}&={3.4\\times10\\times10\\times10\\times10\\times10} \\\\ \\\\ &=340000\\end{align*}[\/latex]<\/p>\n<p>[latex]\\begin{align*} \\text{b. }{2.7\\times 10^{3}}&={2.7\\times10\\times10\\times10} \\\\ \\\\ &=2700\\end{align*}[\/latex]<\/p>\n<p>[latex]\\begin{align*} \\text{c. }{7.1\\times 10^{8}}&={7.1\\times10\\times10\\times10\\times10\\times10\\times10\\times10\\times10} \\\\ \\\\ &=710000000\\end{align*}[\/latex]<\/p>\n<\/div>\n<div class=\"textbox\">\n<p style=\"text-align: center;\">Negative Exponents<\/p>\n<p>number \u00d7 10\u2212<sup>n<\/sup><\/p>\n<p>[latex]\\begin{align*} \\text{a. }{4.2\\times 10^{\u22123}}&=4.2\\times\\dfrac{1}{10^{3}} \\\\ \\\\ &=4.2\\times \\dfrac{1}{10\\times 10\\times 10} \\\\ \\\\\\ &=\\dfrac{4.2}{1000} \\\\ \\\\ &=0.0042\\end{align*}[\/latex]<\/p>\n<p>[latex]\\begin{align*} \\text{b. }{9.3\\times10^{\u22125}}&=9.3\\times\\dfrac{1}{10^{5}} \\\\ \\\\ &=9.3\\times\\dfrac{1}{10\\times10\\times10\\times10\\times10} \\\\ \\\\ &=\\dfrac{9.3}{10\\times10\\times10\\times10\\times10} \\\\ \\\\ &=\\dfrac{9.3}{10000} \\\\ \\\\ &=0.00093\\end{align*}[\/latex]<\/p>\n<p>Here you can see in scientific notation, the number is divided by 10 the same number of times as the number of the exponent.<\/p>\n<\/div>\n<p>When determining what the number is which is represented by scientific notation, you can easily do this just by moving the decimal place over by the number of spaces equal to the exponent. The decimal place will move to the right with positive exponents, making the number larger, and to the left for negative exponents, making the number smaller.<\/p>\n<div class=\"textbox\">\n<p style=\"text-align: center;\">Positive Exponents<\/p>\n<p>Move the decimal to the right to make the number larger.<br \/>\nIn this example, the exponent, or the power, is 5. Move the decimal five places to the right. (The numbers in subscript show the number of places the decimal is moving.)<\/p>\n<p style=\"text-align: center;\">eg. [latex]3.4\\times{10}^{5}[\/latex]\u00a0 = 3.4 <sub style=\"text-align: initial; background-color: initial;\">1<\/sub><span style=\"text-align: initial; background-color: initial; font-size: 1em;\"> 0 <\/span><sub style=\"text-align: initial; background-color: initial;\">2<\/sub><span style=\"text-align: initial; background-color: initial; font-size: 1em;\"> 0 <\/span><sub style=\"text-align: initial; background-color: initial;\">3<\/sub><span style=\"text-align: initial; background-color: initial; font-size: 1em;\"> 0 <\/span><sub style=\"text-align: initial; background-color: initial;\">4<\/sub><span style=\"text-align: initial; background-color: initial; font-size: 1em;\"> 0 <\/span><sub style=\"text-align: initial; background-color: initial;\">5 <\/sub><span style=\"text-align: initial; background-color: initial; font-size: 1em;\">= 340000<\/span><\/p>\n<\/div>\n<div class=\"textbox\">\n<p style=\"text-align: center;\">Negative Exponents<\/p>\n<p>Move the decimal to the left to make the number smaller.<br \/>\nIn this example, the exponent, or the power, is 3. Move the decimal three places to the right.<\/p>\n<p style=\"text-align: center;\">eg. [latex]4.2\\times{10}^{-3}[\/latex] =\u00a0 <sub>3<\/sub> 0\u00a0<sub>2<\/sub> 0\u00a0<sub>1<\/sub> 4 . 2\u00a0 = 0.0042<\/p>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Sample Exercise 5.3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Write [latex]1.7\\times{10^{6}}[\/latex]<sup style=\"text-align: initial;\">\u00a0<\/sup><span style=\"text-align: initial; font-size: 1em;\">in standard form.<\/span><\/p>\n<details open=\"open\">\n<summary><strong>Answers:<\/strong><\/summary>\n<p>[latex]1700000[\/latex]<\/p>\n<p>Move the decimal to the right six places. ([latex]1.7\\times{10^{6}}[\/latex]\u00a0 = 1.7 <sub>1<\/sub> 0 <sub>2<\/sub> 0 <sub>3<\/sub> 0 <sub>4<\/sub> 0 <sub>5 <\/sub>0 <sub>6<\/sub>= [latex]1700000[\/latex])<\/p>\n<\/details>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Key Takeaways<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ul>\n<li>Exponents are helpful when writing very large and very small numbers.<\/li>\n<li>Numbers with positive exponents will be greater or equal to one.<\/li>\n<li>Numbers with negative exponents will be less than one.<\/li>\n<li>When determining the value of a number written in scientific notation, if the power of 10 is positive you move the decimal to the right.<\/li>\n<li>When determining the value of a number written in scientific notation, if the power of 10 is negative you move the decimal to the left.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1>Practice Set 5.1: Determining the numerical value of numbers with positive exponents<\/h1>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Practice Set 5.1: Determining the numerical value of numbers with positive exponents<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Calculate the value of the following numbers with exponents:<\/p>\n<ol class=\"twocolumn\">\n<li>[latex]5^{4}[\/latex]<\/li>\n<li>[latex]2^{7}[\/latex]<\/li>\n<li>[latex]4^{2}[\/latex]<\/li>\n<li>[latex]8^{3}[\/latex]<\/li>\n<li>[latex]6^{6}[\/latex]<\/li>\n<li>[latex]12^{4}[\/latex]<\/li>\n<li>[latex]3^{15}[\/latex]<\/li>\n<li>[latex]9^{5}[\/latex]<\/li>\n<li>[latex]10^{3}[\/latex]<\/li>\n<li>[latex]3^{8}[\/latex]<\/li>\n<\/ol>\n<details>\n<summary><strong>Answers:<\/strong><\/summary>\n<ol class=\"twocolumn\">\n<li>[latex]625[\/latex]<\/li>\n<li>[latex]128[\/latex]<\/li>\n<li>[latex]16[\/latex]<\/li>\n<li>[latex]512[\/latex]<\/li>\n<li>[latex]46656[\/latex]<\/li>\n<li>[latex]20736[\/latex]<\/li>\n<li>[latex]14348907[\/latex]<\/li>\n<li>[latex]59049[\/latex]<\/li>\n<li>[latex]1000[\/latex]<\/li>\n<li>[latex]6561[\/latex]<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<h1>Practice Set 5.2: Determining the numerical value of numbers with negative exponents<\/h1>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Practice Set 5.2: Determining the numerical value of numbers with negative exponents<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Calculate the value of the following numbers with exponents:<\/p>\n<ol class=\"twocolumn\">\n<li>[latex]2^{-4}[\/latex]<\/li>\n<li>[latex]10^{-2}[\/latex]<\/li>\n<li>[latex]4^{-3}[\/latex]<\/li>\n<li>[latex]7^{-4}[\/latex]<\/li>\n<li>[latex]32^{-1}[\/latex]<\/li>\n<li>[latex]5^{-5}[\/latex]<\/li>\n<li>[latex]3^{-5}[\/latex]<\/li>\n<li>[latex]7^{-3}[\/latex]<\/li>\n<li>[latex]8^{-2}[\/latex]<\/li>\n<li>[latex]3.3^{-4}[\/latex]<\/li>\n<\/ol>\n<details>\n<summary><strong>Answers:<\/strong><\/summary>\n<ol class=\"twocolumn\">\n<li>[latex]0.0625[\/latex]<\/li>\n<li>[latex]0.01[\/latex]<\/li>\n<li>[latex]0.015625[\/latex]<\/li>\n<li>[latex]0.00041649312786339[\/latex]<\/li>\n<li>[latex]0.03125[\/latex]<\/li>\n<li>[latex]0.00032[\/latex]<\/li>\n<li>[latex]0.0041152263374486[\/latex]<\/li>\n<li><span id=\"MathJax-Span-52\" class=\"mrow\"><span id=\"MathJax-Span-54\" class=\"mn\">[latex]0.0029154518950437[\/latex]<\/span><\/span><\/li>\n<li>[latex]0.015625[\/latex]<\/li>\n<li><span id=\"MathJax-Span-33\" class=\"mrow\"><span id=\"MathJax-Span-35\" class=\"mn\">[latex]0.0084322648810503[\/latex]<\/span><\/span><\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<h1>Practice Set 5.3: Determining the value of numbers written in scientific notation<\/h1>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Practice Set 5.3: Determining the value of numbers written in scientific notation<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Convert each number to standard form.<\/p>\n<ol class=\"twocolumn\">\n<li>[latex]2.8\\times{10^{4}}[\/latex]<\/li>\n<li>[latex]7.34\\times{10^{-6}}[\/latex]<\/li>\n<li>[latex]4.9\\times{10^{7}}[\/latex]<\/li>\n<li>[latex]5.2\\times{10^{3}}[\/latex]<\/li>\n<li>[latex]1.54\\times{10^{-4}}[\/latex]<\/li>\n<li>[latex]6.241\\times{10^{-8}}[\/latex]<\/li>\n<li>[latex]5.9\\times{10^{5}}[\/latex]<\/li>\n<li>[latex]3.278\\times{10^{-5}}[\/latex]<\/li>\n<li>[latex]4.4\\times{10^{2}}[\/latex]<\/li>\n<li>[latex]8.623\\times{10^{6}}[\/latex]<\/li>\n<\/ol>\n<details>\n<summary><strong>Answers:<\/strong><\/summary>\n<ol class=\"twocolumn\">\n<li>[latex]28000[\/latex]<\/li>\n<li>[latex]0.00000734[\/latex]<\/li>\n<li>[latex]49000000[\/latex]<\/li>\n<li>[latex]5200[\/latex]<\/li>\n<li>[latex]0.000154[\/latex]<\/li>\n<li>[latex]0.00000006241[\/latex]<\/li>\n<li>[latex]590000[\/latex]<\/li>\n<li>[latex]0.0000327[\/latex]<\/li>\n<li>[latex]440[\/latex]<\/li>\n<li>[latex]8623000[\/latex]<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<div class=\"textbox shaded\">This chapter is adapted from Unit 11: Exponents, Roots and Scientific Notation in the book <a href=\"https:\/\/collection.bccampus.ca\/textbooks\/key-concepts-of-intermediate-level-math-bccampus-204\/\"><em>Key Concepts of Intermediate Level Math<\/em><\/a> by Meizhong Wang, licensed as <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0<\/a>.<\/div>\n","protected":false},"author":90,"menu_order":5,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"cc-by"},"chapter-type":[],"contributor":[],"license":[53],"class_list":["post-47","chapter","type-chapter","status-publish","hentry","license-cc-by"],"part":32,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/nursingnumeracy\/wp-json\/pressbooks\/v2\/chapters\/47","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/nursingnumeracy\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/nursingnumeracy\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/nursingnumeracy\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":1,"href":"https:\/\/opentextbc.ca\/nursingnumeracy\/wp-json\/pressbooks\/v2\/chapters\/47\/revisions"}],"predecessor-version":[{"id":48,"href":"https:\/\/opentextbc.ca\/nursingnumeracy\/wp-json\/pressbooks\/v2\/chapters\/47\/revisions\/48"}],"part":[{"href":"https:\/\/opentextbc.ca\/nursingnumeracy\/wp-json\/pressbooks\/v2\/parts\/32"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/nursingnumeracy\/wp-json\/pressbooks\/v2\/chapters\/47\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/nursingnumeracy\/wp-json\/wp\/v2\/media?parent=47"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/nursingnumeracy\/wp-json\/pressbooks\/v2\/chapter-type?post=47"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/nursingnumeracy\/wp-json\/wp\/v2\/contributor?post=47"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/nursingnumeracy\/wp-json\/wp\/v2\/license?post=47"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}