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Convert each percent to a fraction:

  1. 36%
  2. 125%

Solution

36%
Write as a ratio with denominator 100. 36 100
Simplify. 9 25
125%
Write as a ratio with denominator 100. 125 100
Simplify. 5 4
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Convert each percent to a fraction:

  1. 48%
  2. 110%

  1. 12 25
  2. 11 10

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Convert each percent to a fraction:

  1. 64%
  2. 150%

  1. 16 25
  2. 3 2

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The previous example shows that a percent    can be greater than 1 . We saw that 125% means 125 100 , or 5 4 . These are improper fractions, and their values are greater than one.

Convert each percent to a fraction:

  1. 24.5%
  2. 33 1 3 %

Solution

24.5%
Write as a ratio with denominator 100. 24.5 100
Clear the decimal by multiplying numerator and denominator by 10. 24.5 ( 10 ) 100 ( 10 )
Multiply. 245 1000
Rewrite showing common factors. 5 · 49 5 · 200
Simplify. 49 200
33 1 3 %
Write as a ratio with denominator 100. 33 1 3 100
Write the numerator as an improper fraction. 100 3 100
Rewrite as fraction division, replacing 100 with 100 1 . 100 3 ÷ 100 1
Multiply by the reciprocal. 100 3 1 100
Simplify. 1 3
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Convert each percent to a fraction:

  1. 64.4%
  2. 66 2 3 %

  1. 161 250
  2. 2 3

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Convert each percent to a fraction:

  1. 42.5%
  2. 8 3 4 %

  1. 113 250
  2. 7 80

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In Decimals , we learned how to convert fractions to decimals. To convert a percent to a decimal, we first convert it to a fraction and then change the fraction to a decimal.

Convert a percent to a decimal.

  1. Write the percent as a ratio with the denominator 100 .
  2. Convert the fraction to a decimal by dividing the numerator by the denominator.

Convert each percent to a decimal:

  1. 6%
  2. 78%

Solution

Because we want to change to a decimal, we will leave the fractions with denominator 100 instead of removing common factors.

6%
Write as a ratio with denominator 100. 6 100
Change the fraction to a decimal by dividing the numerator by the denominator. 0.06
78%
Write as a ratio with denominator 100. 78 100
Change the fraction to a decimal by dividing the numerator by the denominator. 0.78
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Convert each percent to a decimal:

  1. 9%
  2. 87%

  1. 0.09
  2. 0.87

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Convert each percent to a decimal:

  1. 3%
  2. 91%

  1. ⓐ 0.03
  2. ⓑ 0.91

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Convert each percent to a decimal:

  1. 135%
  2. 12.5%

Solution

135%
Write as a ratio with denominator 100. 135 100
Change the fraction to a decimal by dividing the numerator by the denominator. 1.35
12.5%
Write as a ratio with denominator 100. 12.5 100
Change the fraction to a decimal by dividing the numerator by the denominator. 0.125
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Convert each percent to a decimal:

  1. 115%
  2. 23.5%

  1. ⓐ 1.15
  2. ⓑ 0.235

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Convert each percent to a decimal:

  1. 123%
  2. 16.8%

  1. ⓐ 1.23
  2. ⓑ 0.168

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Let's summarize the results from the previous examples in [link] , and look for a pattern we could use to quickly convert a percent number to a decimal number.

Percent Decimal
6% 0.06
78% 0.78
135% 1.35
12.5% 0.125

Do you see the pattern?

To convert a percent    number to a decimal number, we move the decimal point two places to the left and remove the % sign. (Sometimes the decimal point does not appear in the percent number, but just like we can think of the integer 6 as 6.0 , we can think of 6% as 6.0% . ) Notice that we may need to add zeros in front of the number when moving the decimal to the left.

[link] uses the percents in [link] and shows visually how to convert them to decimals by moving the decimal point two places to the left.

Practice Key Terms 1

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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