# Writing Decimals and Fractions as Percents

### Learning Outcomes

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

### Convert a decimal to a percent.

- Write the decimal as a fraction.
- If the denominator of the fraction is not [latex]100[/latex], rewrite it as an equivalent fraction with denominator [latex]100[/latex].
- Write this ratio as a percent.

### example

Convert each decimal to a percent: 1. [latex]0.05[/latex] 2.[latex]0.83[/latex] Solution1. | |

[latex]0.05[/latex] | |

Write as a fraction. The denominator is [latex]100[/latex]. | [latex]{\Large\frac{5}{100}}[/latex] |

Write this ratio as a percent. | [latex]5[/latex]% |

2. | |

[latex]0.83[/latex] | |

The denominator is [latex]100[/latex]. | [latex]{\Large\frac{83}{100}}[/latex] |

Write this ratio as a percent. | [latex]83[/latex]% |

### try it

[ohm_question]146666[/ohm_question]### example

Convert each decimal to a percent: 1. [latex]1.05[/latex] 2. [latex]0.075[/latex]Answer: Solution

1. | |

[latex]0.05[/latex] | |

Write as a fraction. | [latex]1{\Large\frac{5}{100}}[/latex] |

Write as an improper fraction. The denominator is [latex]100[/latex]. | [latex]{\Large\frac{105}{100}}[/latex] |

Write this ratio as a percent. | [latex]105[/latex]% |

2. | |

[latex]0.075[/latex] | |

Write as a fraction. The denominator is [latex]1,000[/latex]. | [latex]{\Large\frac{75}{1,000}}[/latex] |

Divide the numerator and denominator by [latex]10[/latex], so that the denominator is [latex]100[/latex]. | [latex]{\Large\frac{7.5}{100}}[/latex] |

Write this ratio as a percent. | [latex]7.5[/latex]% |

### try it

[ohm_question]146667[/ohm_question] [ohm_question]146668[/ohm_question]Decimal | Percent |
---|---|

[latex]0.05[/latex] | [latex]\text{5%}[/latex] |

[latex]0.83[/latex] | [latex]\text{83%}[/latex] |

[latex]1.05[/latex] | [latex]\text{105%}[/latex] |

[latex]0.075[/latex] | [latex]\text{7.5%}[/latex] |

### Convert a fraction to a percent

- Convert the fraction to a decimal.
- Convert the decimal to a percent.

### example

Convert each fraction or mixed number to a percent: 1. [latex]{\Large\frac{3}{4}}[/latex] 2. [latex]{\Large\frac{11}{8}}[/latex] 3. [latex]2{\Large\frac{1}{5}}[/latex]Answer: Solution To convert a fraction to a decimal, divide the numerator by the denominator.

1. | [latex]{\Large\frac{3}{4}}[/latex] |

Change to a decimal. | |

Write as a percent by moving the decimal two places. | [latex]75[/latex]% |

2. | [latex]{\Large\frac{11}{8}}[/latex] |

Change to a decimal. | |

Write as a percent by moving the decimal two places. | [latex]137.5[/latex]% |

3. | [latex]2{\Large\frac{1}{5}}[/latex] |

Write as an improper fraction. | [latex]{\Large\frac{11}{5}}[/latex] |

Change to a decimal. | |

Write as a percent. | [latex]220[/latex]% |

Answer: Solution To change a fraction to a decimal, we divide the numerator by the denominator.

[latex]\Large\frac{5}{7}[/latex] | |

Change to a decimal—rounding to the nearest thousandth. | [latex]0.714[/latex] |

Write as a percent. | [latex]71.4[/latex]% |

### try it

[ohm_question]146669[/ohm_question] [ohm_question]146670[/ohm_question] [ohm_question]146671[/ohm_question]Fraction | Decimal | Percent |
---|---|---|

[latex]{\Large\frac{3}{4}}[/latex] | [latex]0.75[/latex] | [latex]75[/latex]% |

[latex]{\Large\frac{11}{8}}[/latex] | [latex]1.375[/latex] | [latex]137.5[/latex]% |

[latex]2{\Large\frac{1}{5}} ={\Large\frac{11}{5}}[/latex] | [latex]2.20[/latex] | [latex]220[/latex]% |

## Licenses & Attributions

### CC licensed content, Original

- Question ID 146671, 146670, 146669, 146668, 146667.
**Authored by:**Lumen Learning.**License:**CC BY: Attribution.**License terms:**IMathAS Community License CC-BY + GPL.

### CC licensed content, Specific attribution

- Prealgebra.
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