# How to change fraction to percent?

Turns a fraction or mixed number into a percent: the exact percent when its decimal ends (5/8 is 62.5%), or rounded to the places you pick (1/3 is about 33.33%).

- Page: https://www.acalculator.org/math/fraction-to-percentage
- JSON spec: https://www.acalculator.org/math/fraction-to-percentage.json
- Version: f9b557e5ba51

## Default answer

Example with the default inputs (Fraction 5/8, Round to (decimal places) 2): 5/8 = 5 ÷ 8 = 0.625; 0.625 × 100 = 62.5%.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| f | Fraction | A fraction, mixed number, or whole number, such as 5/8, 1 3/4, or 2/3. |
| dp | Round to (decimal places) | How many decimal places the rounded percent keeps, from 0 to 10. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| percent | Percent | The exact percent when its decimal ends; otherwise the rounded percent after ≈. |
| rounded | Rounded percent | The percent rounded to the chosen decimal places; halves round away from zero. |
| decimal | Decimal | The fraction as a decimal: exact when it ends, else rounded to 2 more places than the percent. |
| exact | Exact? | Yes when the decimal ends, so the percent is exact; no when it repeats. |
| work | How | The fraction divided out, then times 100. |

## Method

percent = numerator ÷ denominator × 100. The decimal ends when the denominator in lowest terms has no prime factor other than 2 and 5; then the percent is exact. Otherwise it is rounded, halves away from zero.

## Assumptions

- The fraction is reduced to lowest terms first; all arithmetic is exact.
- A rounded percent keeps exactly the chosen number of decimal places; halves round away from zero.

## Worked examples

1. f = 5/8, dp = 2 gives percent = 62.5%, rounded = 62.50%, decimal = 0.625, exact = yes, work = 5/8 = 5 ÷ 8 = 0.625; 0.625 × 100 = 62.5%. Source: OpenStax, Prealgebra 2e, §6.1 Understand Percent (convert a fraction to a percent: write it as a decimal, then multiply by 100), https://openstax.org/books/prealgebra-2e/pages/6-1-understand-percent (retrieved 2026-10-05).
2. f = 1/3, dp = 2 gives percent = ≈ 33.33%, decimal = 0.3333, exact = no, the decimal repeats. Source: OpenStax, Prealgebra 2e, §6.1 Understand Percent (convert a fraction to a percent: write it as a decimal, then multiply by 100), https://openstax.org/books/prealgebra-2e/pages/6-1-understand-percent (retrieved 2026-10-05).
3. f = 2/3, dp = 1 gives percent = ≈ 66.7%, rounded = 66.7%. Source: OpenStax, Prealgebra 2e, §6.1 Understand Percent (convert a fraction to a percent: write it as a decimal, then multiply by 100), https://openstax.org/books/prealgebra-2e/pages/6-1-understand-percent (retrieved 2026-10-05).
4. f = 1 3/4, dp = 0 gives percent = 175%, rounded = 175%, decimal = 1.75. Source: OpenStax, Prealgebra 2e, §6.1 Understand Percent (convert a fraction to a percent: write it as a decimal, then multiply by 100), https://openstax.org/books/prealgebra-2e/pages/6-1-understand-percent (retrieved 2026-10-05).
5. f = -1/8, dp = 1 gives percent = −12.5%, rounded = −12.5%, decimal = −0.125. Source: OpenStax, Prealgebra 2e, §6.1 Understand Percent (convert a fraction to a percent: write it as a decimal, then multiply by 100), https://openstax.org/books/prealgebra-2e/pages/6-1-understand-percent (retrieved 2026-10-05).
6. f = 1/16, dp = 0 gives percent = 6.25%, rounded = 6%. Source: OpenStax, Prealgebra 2e, §6.1 Understand Percent (convert a fraction to a percent: write it as a decimal, then multiply by 100), https://openstax.org/books/prealgebra-2e/pages/6-1-understand-percent (retrieved 2026-10-05).

## FAQ

### How do you change a fraction to a percent?

Divide the top by the bottom, then multiply by 100. 5/8 = 5 ÷ 8 = 0.625, and 0.625 × 100 = 62.5%.

### What is 1/3 as a percent?

1 ÷ 3 = 0.333…, so 1/3 is 33.333…%, about 33.33% to two decimal places. The 3s never end.

### When is the percent exact?

When the bottom number, in lowest terms, has no prime factors other than 2 and 5 (such as 4, 8, 20 or 25). Then the decimal ends. Any other factor, such as 3 or 7, gives a repeating decimal.

### How do I convert a mixed number?

Write it as an improper fraction first: 1 3/4 = 7/4 = 1.75 = 175%. A fraction above 1 is more than 100%.

### Is there a shortcut for fractions over 100?

Yes: a fraction over 100 is already a percent. 37/100 is 37%. For 3/20 you can also scale the bottom to 100: 3/20 = 15/100 = 15%.

### How does the page round?

It keeps the number of decimal places you choose and rounds a half away from zero: 66.666…% to one place is 66.7%.

## Sources

- OpenStax, Prealgebra 2e, §6.1 Understand Percent: to convert a fraction to a percent, convert the fraction to a decimal, then convert the decimal to a percent (multiply by 100). CC BY 4.0. Retrieved 2026-10-05. https://openstax.org/books/prealgebra-2e/pages/6-1-understand-percent
- OpenStax, Prealgebra 2e, §5.3 Decimals and Fractions: a fraction as a decimal by dividing; repeating decimals. CC BY 4.0. Retrieved 2026-10-05. https://openstax.org/books/prealgebra-2e/pages/5-3-decimals-and-fractions