# Writing Percents as Fractions and Decimals

### Learning Outcomes

- Convert a percent to a fraction
- Convert a percent to a decimal

## Percents [latex]\longrightarrow[/latex] Fractions

Since percents are ratios, they can easily be expressed as fractions. Remember that percent means per [latex]100[/latex], so the denominator of the fraction is [latex]100[/latex].### Convert a percent to a fraction

- Write the percent as a ratio with the denominator [latex]100[/latex].
- Simplify the fraction if possible.

### example

Convert each percent to a fraction: 1. [latex]\text{36%}[/latex] 2. [latex]\text{125%}[/latex] Solution1. | |

[latex]36\%[/latex] | |

Write as a ratio with denominator [latex]100[/latex]. | [latex]{\Large\frac{36}{100}}[/latex] |

Simplify. | [latex]{\Large\frac{9}{25}}[/latex] |

2. | |

[latex]125\%[/latex] | |

Write as a ratio with denominator [latex]100[/latex]. | [latex]{\Large\frac{125}{100}}[/latex] |

Simplify. | [latex]{\Large\frac{5}{4}}[/latex] |

### try it

[ohm_question]146657[/ohm_question] [ohm_question]146660[/ohm_question]### Example

Convert each percent to a fraction: 1. [latex]\text{24.5%}[/latex] 2. [latex]33\Large\frac{1}{3}\normalsize\%[/latex] Solution1. | |

[latex]24.5\%[/latex] | |

Write as a ratio with denominator [latex]100[/latex]. | [latex]{\Large\frac{24.5}{100}}[/latex] |

Clear the decimal by multiplying numerator and denominator by [latex]10[/latex]. | [latex]{\Large\frac{24.5\left(10\right)}{100\left(10\right)}}[/latex] |

Multiply. | [latex]{\Large\frac{245}{1000}}[/latex] |

Rewrite showing common factors. | [latex]{\Large\frac{5\cdot {49}}{5\cdot {200}}}[/latex] |

Simplify. | [latex]{\Large\frac{49}{200}}[/latex] |

2. | |

[latex]33\Large\frac{1}{3}\normalsize\%[/latex] | |

Write as a ratio with denominator [latex]100[/latex]. | [latex]{\Large\frac{33\Large\frac{1}{3}}{100}}[/latex] |

Write the numerator as an improper fraction. | [latex]{\Large\frac{\frac{100}{3}}{100}}[/latex] |

Rewrite as fraction division, replacing [latex]100[/latex] with [latex]\frac{100}{1}[/latex] | [latex]{\Large\frac{100}{3}}\div {\Large\frac{100}{1}}[/latex] |

Multiply by the reciprocal. | [latex]{\Large\frac{100}{3}} \cdot {\Large\frac{1}{100}}[/latex] |

Simplify. | [latex]{\Large\frac{1}{3}}[/latex] |

### try it

[ohm_question]146658[/ohm_question] [ohm_question]146659[/ohm_question]## Percents[latex]\longrightarrow[/latex] 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

- Write the percent as a ratio with the denominator [latex]100[/latex].
- Convert the fraction to a decimal by dividing the numerator by the denominator.

### example

Convert each percent to a decimal: 1. [latex]\text{6%}[/latex] 2. [latex]\text{78%}[/latex]Answer: Solution Because we want to change to a decimal, we will leave the fractions with denominator [latex]100[/latex] instead of removing common factors.

1. | |

[latex]6\%[/latex] | |

Write as a ratio with denominator [latex]100[/latex]. | [latex]{\Large\frac{6}{100}}[/latex] |

Change the fraction to a decimal by dividing the numerator by the denominator. | [latex]0.06[/latex] |

2. | |

[latex]78\%[/latex] | |

Write as a ratio with denominator [latex]100[/latex]. | [latex]{\Large\frac{78}{100}}[/latex] |

Change the fraction to a decimal by dividing the numerator by the denominator. | [latex]0.78[/latex] |

### try it

Convert each percent to a decimal: 1. [latex]\text{9%}[/latex] 2. [latex]\text{87%}[/latex]Answer: 1. [latex]0.09[/latex] 2. [latex]0.87[/latex]

### example

Convert each percent to a decimal: 1. [latex]\text{135%}[/latex] 2. [latex]\text{12.5%}[/latex] Solution1. | |

[latex]135\%[/latex] | |

Write as a ratio with denominator [latex]100[/latex]. | [latex]{\Large\frac{135}{100}}[/latex] |

Change the fraction to a decimal by dividing the numerator by the denominator. | [latex]1.35[/latex] |

2. | |

[latex]12.5\%[/latex] | |

Write as a ratio with denominator [latex]100[/latex]. | [latex]{\Large\frac{12.5}{100}}[/latex] |

Change the fraction to a decimal by dividing the numerator by the denominator. | [latex]0.125[/latex] |

### try it

[ohm_question]146661[/ohm_question] [ohm_question]146662[/ohm_question]Percent | Decimal |
---|---|

[latex]\text{6%}[/latex] | [latex]0.06[/latex] |

[latex]\text{78%}[/latex] | [latex]0.78[/latex] |

[latex]\text{135%}[/latex] | [latex]1.35[/latex] |

[latex]\text{12.5%}[/latex] | [latex]0.125[/latex] |

### example

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

Answer: Solution

1. | |

[latex]77\%[/latex] | |

Write as a ratio with denominator [latex]100[/latex]. | [latex]{\Large\frac{77}{100}}[/latex] |

2. | |

[latex]\Large\frac{77}{100}[/latex] | |

Change the fraction to a decimal by dividing the numerator by the denominator. | [latex]0.77[/latex] |

### 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 [latex]\text{25%}[/latex]. Convert the percent to: 1. a fraction 2. a decimal Solution1. | |

[latex]25\%[/latex] | |

Write as a ratio with denominator [latex]100[/latex]. | [latex]{\Large\frac{25}{100}}[/latex] |

Simplify. | [latex]{\Large\frac{1}{4}}[/latex] |

2. | [latex]{\Large\frac{1}{4}}[/latex] |

Change the fraction to a decimal by dividing the numerator by the denominator. | [latex]0.25[/latex] |

(credit: Riles32807, Wikimedia Commons)

### try it

[ohm_question]146665[/ohm_question]Percent | Decimal | Fraction |
---|---|---|

[latex]\text{6%}[/latex] | [latex]0.06[/latex] | [latex]{\Large\frac{3}{50}}[/latex] |

[latex]\text{78%}[/latex] | [latex]0.78[/latex] | [latex]{\Large\frac{39}{50}}[/latex] |

[latex]\text{135%}[/latex] | [latex]1.35[/latex] | [latex]{\Large\frac{27}{20}}[/latex] |

[latex]\text{12.5%}[/latex] | [latex]0.125[/latex] | [latex]{\Large\frac{1}{8}}[/latex] |

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- Question ID: 146665, 146664, 146665, 146663, 146662, 146661.
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- Prealgebra.
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