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Guides d'étude > Prealgebra

Writing Percents as Fractions and Decimals

Learning Outcomes

  • Convert a percent to a fraction
  • Convert a percent to a decimal

Percents ----> Fractions

Since percents are ratios, they can easily be expressed as fractions. Remember that percent means per 100100, so the denominator of the fraction is 100100.

Convert a percent to a fraction

  1. Write the percent as a ratio with the denominator 100100.
  2. Simplify the fraction if possible.
 

example

Convert each percent to a fraction: ⓐ \text{36%} ⓑ \text{125%} Solution
ⓐ
3636%
Write as a ratio with denominator 100100. 36100\frac{36}{100}
Simplify. 925\frac{9}{25}
ⓑ
125125%
Write as a ratio with denominator 100100. 125100\frac{125}{100}
Simplify. 54\frac{5}{4}
 
 

try it

[ohm_question]146657[/ohm_question] [ohm_question]146660[/ohm_question]
The previous example shows that a percent can be greater than 11. We saw that \text{125%} means 125100\frac{125}{100}, or 54\frac{5}{4}. These are improper fractions, and their values are greater than one.

Example

Convert each percent to a fraction: ⓐ \text{24.5%} ⓑ 331333\frac{1}{3}% Solution
ⓐ
24.524.5%
Write as a ratio with denominator 100100. 24.5100\frac{24.5}{100}
Clear the decimal by multiplying numerator and denominator by 1010. 24.5(10)100(10)\frac{24.5\left(10\right)}{100\left(10\right)}
Multiply. 2451000\frac{245}{1000}
Rewrite showing common factors. 5⋅495⋅200\frac{5\cdot 49}{5\cdot 200}
Simplify. 49200\frac{49}{200}
ⓑ
331333\frac{1}{3}%
Write as a ratio with denominator 100100. 3313100\frac{33\frac{1}{3}}{100}
Write the numerator as an improper fraction. 1003100\frac{\frac{100}{3}}{100}
Rewrite as fraction division, replacing 100100 with 1001\frac{100}{1} . 1003÷1001\frac{100}{3}\div \frac{100}{1}
Multiply by the reciprocal. 1003⋅1100\frac{100}{3}\cdot \frac{1}{100}
Simplify. 13\frac{1}{3}
 
 

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[ohm_question]146658[/ohm_question] [ohm_question]146659[/ohm_question]

Percents ----> Decimals

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 100100.
  2. Convert the fraction to a decimal by dividing the numerator by the denominator.
 

example

Convert each percent to a decimal: ⓐ \text{6%} ⓑ \text{78%}

Answer: Solution Because we want to change to a decimal, we will leave the fractions with denominator 100100 instead of removing common factors.

ⓐ
66%
Write as a ratio with denominator 100100. 6100\frac{6}{100}
Change the fraction to a decimal by dividing the numerator by the denominator. 0.060.06
ⓑ
7878%
Write as a ratio with denominator 100100. 78100\frac{78}{100}
Change the fraction to a decimal by dividing the numerator by the denominator. 0.780.78

 

try it

#903903 (only 22 digits %) # Convert each percent to a decimal: ⓐ \text{9%} ⓑ \text{87%} ⓐ 0.090.09 ⓑ 0.870.87 OHM: 903

example

Convert each percent to a decimal: ⓐ \text{135%} ⓑ \text{12.5%} Solution
ⓐ
135135%
Write as a ratio with denominator 100100. 135100\frac{135}{100}
Change the fraction to a decimal by dividing the numerator by the denominator. 1.351.35
ⓑ
12.512.5%
Write as a ratio with denominator 100100. 12.5100\frac{12.5}{100}
Change the fraction to a decimal by dividing the numerator by the denominator. 0.1250.125
 
   

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[ohm_question]146661[/ohm_question] [ohm_question]146662[/ohm_question]
  Let's summarize the results from the previous examples in the table below, and look for a pattern we could use to quickly convert a percent number to a decimal number.
Percent Decimal
\text{6%} 0.060.06
\text{78%} 0.780.78
\text{135%} 1.351.35
\text{12.5%} 0.1250.125
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 66 as 6.06.0, we can think of \text{6%} as \text{6.0%}. ) Notice that we may need to add zeros in front of the number when moving the decimal to the left. The next table uses the percents in the table above and shows visually how to convert them to decimals by moving the decimal point two places to the left. The figures shows two columns and five rows . The first row is a header row and it labels each column

example

Among a group of business leaders, \text{77%} believe that poor math and science education in the U.S. will lead to higher unemployment rates. Convert the percent to: ⓐ a fraction ⓑ a decimal

Answer: Solution

ⓐ
7777%
Write as a ratio with denominator 100100. 77100\frac{77}{100}
ⓑ
77100\frac{77}{100}
Change the fraction to a decimal by dividing the numerator by the denominator. 0.770.77

 

try it

[ohm_question]146663[/ohm_question] [ohm_question]146664[/ohm_question]

Example

There are four suits of cards in a deck of cards—hearts, diamonds, clubs, and spades. The probability of randomly choosing a heart from a shuffled deck of cards is \text{25%}. Convert the percent to: ⓐ a fraction ⓑ a decimal Solution
ⓐ
2525%
Write as a ratio with denominator 100100. 25100\frac{25}{100}
Simplify. 14\frac{1}{4}
ⓑ 14\frac{1}{4}
Change the fraction to a decimal by dividing the numerator by the denominator. 0.250.25
 
  (credit: Riles32807, Wikimedia Commons) The figure shows someone holding a deck of cards.

try it

[ohm_question]146665[/ohm_question]
In summary, here is the table from above with conversions of percents to fractions added.
Percent Decimal Fraction
\text{6%} 0.060.06 350\frac{3}{50}
\text{78%} 0.780.78 3950\frac{39}{50}
\text{135%} 1.351.35 2720\frac{27}{20}
\text{12.5%} 0.1250.125 18\frac{1}{8}
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