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Unit 2: Percent

Topic A: Introducing Percent

Reading and Writing Percents

To write a percent:

  • Write the number in the usual way
  • Place the percent sign after the numerals
    • 50%
    • 512% or 5.5%
    • 34% or 0.75%

To read a percent:

  • Read the numbers in the usual way
  • Say “percent” after the number
    • 16%: say “sixteen percent”
    • 412%: say “four and one-half percent”
    • 0.25%: say “twenty-five hundredths percent,” or “one-quarter percent,” or “point two five percent”

Exercise 1

Write these percents using numerals and a percent sign. Note that the mixed numbers may be expressed with common fractions or decimals.

  1. Thirty-four percent          34%
  2. Twelve percent
  3. Four-fifths percent
  4. One hundred sixteen and three-tenths percent
  5. Thirteen percent
  6. Six and one-fifth percent
  7. Ninety-four and one-half percent

Answers to Exercise 1

  1. 12%
  2. 0.8% or 45%
  3. 116.3% or 116310%
  4. 13%
  5. 6.2% or 615%
  6. 94.5% or 9412%

Exercise 2

Write these percents using words.

  1. 62%: sixty-two percent
  2. 3712%
  3. 202%
  4. 34%
  5. 18.3%
  6. 1412%
  7. 10012%

Answers to Exercise 2

  1. Thirty-seven and one-half percent
  2. Two hundred two percent
  3. Three-quarters percent
  4. Eighteen and three-tenths percent
  5. Fourteen and one-half percent
  6. One hundred one percent

Changing Decimals to Percents

Writing equivalent fractions is an important math skill.

Equivalent common fractions, decimals, and percents all represent the same amount.

Equivalent fractions, decimals, and percentages
Fractions Decimals Percentages
12 0.5 50%
310 0.3 30%

You need the skill of writing equivalent fractions for working with percents.

To change any number to a percent, multiply the number by 100% and place a percent sign % after the product.

Remember this shortcut for multiplying by 100?

4.27×100=427
0.287×100=28.7
53×100=5300

The shortcut is: When multiplying by 100, move the decimal point two places to the right.

Example A

Change these numbers to a percent.
1        1×100%    =    100%0.25       0.25×100%    =    25%0.8       0.8×100%    =    80%0.375       0.375×100%    =    37.5%

So…

To change a decimal to a percent, move the decimal point two places to the right and then write the percent sign after the number.

Example B

Change each decimal to a percent.
0.125=0.125=12.5%
1.375=1.375=137.5%

If the decimal point moves to the end of the number it is not necessary to write the decimal point. Remember that zeros at the beginning of a number are also not necessary.

0.24=0.24=0.24%=24%

0.05=0.05=0.05%=5%

If the decimal is a tenth (one decimal place), it will be necessary to add a zero. If you are changing a whole number to a percent, add two zeros.

0.4=0.40=40%

1.7=1.70=170%

2=2.00=200%

Exercise 3

Change these decimals to percents.

Decimal × 100%
Move decimal 2 places to right
= Percent
A. 0.75 0.75 =75%
B. 0.33
C. 0.1
D. 0.0025
E. 0.9
F. 0.325
G. 0.0625
H. 3

Answers to Exercise 3

  1. 33%
  2. 10%
  3. 0.25%
  4. 90%
  5. 32.5%
  6. 6.25%
  7. 300%

Changing Percents to Decimals

Review dividing by 100:

47.39÷100=0.4739
429÷100=4.29
3.824÷100=0.03824

To divide by 100, move the decimal point two places to the left.

Example A

Change each percent to a decimal or mixed number.

58%  =  58÷100  =  .58  =  0.5820%  =  20÷100  =  .2  =  0.26%  =  6÷100  =  .06  =  0.06110%  =  110÷100  =  1.10

So…

To change a percent to a decimal, divide by 100 (move the decimal point two places to the left) and remove the percent sign.

Example B

Change each percent to a decimal.

75%  =  75.0%  =  0.7512%  =  12.0%  =  0.1237.5%  =  37.5%  =  0.375125%  =  125.0%  =  1.255%  =  5.0%  =  0.054.6%  =  4.6%  =  0.046

Some notes to remember:

  • If there is no decimal point in the percent, place the decimal point after the last numeral and then divide by 100. 24%=24.0%=0.24
  • It may be necessary to prefix zeros. (This means adding zeros in front of the number, if needed). 6%=6.0%=0.06
  • A zero at the right of a decimal is not needed and may be left off. 40%=40.0%=0.40=0.4

Exercise 4

Change each percent to its decimal equivalent.

Percent ÷ 100%
Move decimal 2 places to left
= Decimal
A. 23%  23. =0.23
B. 1%
C. 112%
D. 10.3%
E. 36%
F. 147%

Answers to Exercise 4

  1. 0.01
  2. 1.12
  3. 0.103
  4. 0.36
  5. 1.47

To change a percent containing a common fraction to a decimal, do this:

  • Change the common fraction in the percent to a decimal in the percent.
  • Divide by 100 (move the decimal 2 places to the left).

Example C

Let’s convert these percents containing common fractions into decimals:

312%  =  3.5%       3.5%÷100 =.035=0.0353712%  =  37.5%       37.5%÷100 =.375=0.37514%  =  0.25%       0.25%÷100 =.00251713%  =  17.¯3%       17.¯3%÷100 =0.17¯3

Exercise 5

Change each percent to its decimal equivalent.

  1. 845%=     8.8%=0.088
  2. 412%=
  3. 5634%=
  4. 135%=
  5. 11212%=
  6. 238%=
  7. 514%=

Answers to Exercise 5

  1. 0.045
  2. 0.5675
  3. 0.016
  4. 1.125
  5. 0.02375
  6. 0.0525

Changing Common Fractions to Percents

To change any number to a percent, multiply the number by 100% and place the percent sign % after the product.

There are two methods you can use to change a common fraction to a percent.

Method One

To change a common fraction to an equivalent percent, multiply the common fraction by 100%.

Example A

34=_____%
34
Multiply by 100% 34×100%
Convert 100% to a fraction. 34×1001%
Simplify the fractions by dividing the numerator and denominator by 4. 341×100251%
The 4 cancels and 100 is reduced to 25. 31×251%
Multiply 3 by 25%. 3×25%
75%
115=_____%
115
Convert number to a fraction. 65
Multiply by 100%. 65×100%
Convert 100% to a fraction. 65×1001%
Simplify the fractions by dividing the denominator and numerator by 5. 651×100201%
The 5 cancels and 100 is reduced to 20. 61×201%
Multiply 6 by 20%. 6×20%
120%

Exercise 6

Multiply by 100% to change each common fraction to an equivalent percent.

  1. 45          45×100%=80%
  2. 15=
  3. 910=
  4. 112=
  5. 710=
  6. 334=
  7. 12=

Answers to Exercise 6

  1. 20%
  2. 90%
  3. 150%
  4. 70%
  5. 375%
  6. 50%

Method Two

To change a common fraction to an equivalent percent, first write the common fraction as a decimal. Then multiply the decimal by 100% (move the decimal point two places to the right).

Example A

  1. 38=_____%
  2. Use long division to write the fraction as a decimal.
  3. 38=0.375
  4. Move the decimal two spots to the right.
    0.375=37.5
Convert 38 to a percentage
38=_____%
Use long division to write fraction as a decimal. A long division equation showing that 3 divided by 8 equals 0.375.
38=0.375
Move the decimal point two places to the right and add the percent sign. 0.375=37.5%
Convert 13 to a percentage
13=_____%
Use long division to write fraction as a decimal. A long division equation showing that 1 divided by 3 equals 0.333 repeating.
13=0.33¯3
Move the decimal point two places to the right and add the percent sign. 0.33¯3=33.¯3% also written as 3313%
Convert 1112 to a percentage
1112=_____%
Use long division to write fraction as a decimal. A long division equation showing that 11 divided by 12 equals 0.9166 repeating.
1112=0.91¯6
 Move the decimal point two places to the right and add the percent sign. 0.916¯6=91.¯6%

Exercise 7

  1. 112=0.08¯3      0.08¯3×100%=8.¯3%
  2. 18
  3. 58
  4. 78
  5. 23
  6. 516
  7. 56
  8. 49

Answers to Exercise 7

  1. 12.5%
  2. 62.5%
  3. 87.5%
  4. 66.¯6%
  5. 31.25%
  6. 83.¯3%
  7. 44.¯4%

The method you use to change a common fraction to a percent will depend on the numbers you are working with. Choose whichever method seems easier for the situation. You will also memorize many equivalencies as you work with them. But you should definitely memorize:

  • 13=3313%
  • 23=6623%

Changing Percents to Common Fractions

You know that percents are a form of fraction with an unwritten denominator of 100. A % sign is used.

To change any percent to a decimal, common fraction, or mixed number, divide by 100 and remove the percent sign.

To change a percent to a common fraction:

  • Write the numerals in the percent as the numerator.
  • Write 100 as the denominator. (Remember that the line in a fraction can be a divided by sign, so 58%=58100 is the same as 58÷100.)
  • Remove the % sign.
  • Simplify the fraction: 58100=2950

Example A

Write each percent as a common fraction.

38%=38100÷(22)=38÷2100÷2=1950

25%=25100÷(2525)=25÷25100÷25=14

3%=3100

Note that percents greater than or equal to 100 become improper fractions which will be rewritten as mixed numbers.

Here is an example:

110%=110100=110100=1110

1100110100_10

Here is another example:

120%=120100=120100=115

1100120100_20

Remember 100% is the whole thing: 100%=1.

Exercise 8

Change each percent to a common fraction. Simplify to lowest terms.

  1. 31%=
  2. 11%=
  3. 2%=
  4. 20%=
  5. 75%=
  6. 100%=
  7. 750%=

Answers to Exercise 8

  1. 31100
  2. 11100
  3. 150
  4. 15
  5. 34
  6. 1
  7. 712

Percents Less Than 1%

Sometimes a percent smaller than 1% is used. For example, you will hear amounts such as 14% or 18% or 12% on the news about the Bank of Canada rate and the rise and fall of inflation. These are small amounts. Sometimes the expression “12 of a percentage point” is used instead of “12%”.

What is 14%?

14% is 14 of 1%

1%=1100, so 14 of 1%=14×1100=1400

14%=0.25%=0.0025

What is 12%?

12%=12 of 1%=12×1100=1200

12%=0.5%=0.005

To work with percents less than 1%, change the percent to a decimal by dividing by 100 (move decimal point two places to the left).

0.2%=0.002

0.75%=0.0075

If the percent is expressed as a common fraction, do this:

  • Write the common fraction percent as a decimal percent.
  • Divide by 100 (move decimal point two places left).

12%=0.5%=0.00514%=0.0025%=0.002518%=0.00125% =0.00125

Exercise 9

Change each percent to an equivalent decimal.

  1. 12%=
  2. 0.6%=
  3. 310%=
  4. 35%=
  5. 0.75%=
  6. 34%=
  7. 0.5%=
  8. 14%=
  9. 0.125%=
  10. 58%=

Answers to Exercise 9

  1. 0.005
  2. 0.006
  3. 0.003
  4. 0.006
  5. 0.0075
  6. 0.0075
  7. 0.005
  8. 0.0025
  9. 0.00125
  10. 0.00625

16⅔%, 33⅓%, 66⅔%, 83⅓% …

These percents will become repeating decimals. For example:

3313%=33.¯3%=0.33¯36623%=66.¯6%=0.66¯6

It is usually more convenient to use the common fraction equivalent of these percents. Memorize them, or make a note on a special paper and post it near your work space.

3313%=3313÷100=1003×1100 =136623%=6623÷100=2003×1100 =23

1623%=163313%=136623%=238313%=56

Review of Equivalent Common Fractions, Decimals, and Percents

Complete this chart. These are equivalents that you will often use, so use this chart for reference. Memorize as many equivalents as you can. You may wish to put other equivalents on the chart.

Common Fraction Decimal Percent
14
0.5
75%
18
0.375
62.5%

Answers to Review of Equivalent Common Fractions, Decimals, and Percents

Common Fraction Decimal Percent
14 0.25 25%
12 0.5 50%
34 0.75 75%
18 0.125 12.5%
38 0.375 37.5%
58 0.625 62.5%

Topic A: Self-Test

Mark       /15                  Aim        13/15

  1. Write these percents in numeral form. (2 marks)
    1. Sixty-two and one-half percent
    2. One hundred six and one-fifth percent
  2. Write these percents in words. (2 marks)
    1. 72%
    2. 34%
  3. Change the percents to decimal fractions. (5 marks)
    1. 32%
    2. 18.5%
    3. 125%
    4. 45%
    5. 23%
  4. Change these percents to common fractions in lowest terms. (4 marks)
    1. 16%
    2. 20%
    3. 106%
    4. 75%
  5. Change these common fractions to equivalent percents. (2 marks)
    1. 45
    2. 38

Answers to Topic A Self-Test

    1. 62.5% or 6212%
    2. 106.2% or 10615%
    1. Seventy-two percent
    2. Three-quarters percent
    1. 0.32
    2. 0.185
    3. 1.25
    4. 0.008
    5. 0.00¯6
    1. 425
    2. 15
    3. 1350
    4. 34
    1. 80%
    2. 37.5%

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Adult Literacy Fundamental Mathematics: Book 6 - 2nd Edition Copyright © 2022 by Liz Girard and Wendy Tagami is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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