Percent to Fraction Converter
Converts between percentages, fractions and decimals, in every direction, in lowest terms.
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Your details
Result
- As a fraction
- 5/8
- As a percentage
- 62.5%
- As a decimal
- 0.625
- Out of 1000
- 625 per mille
In lowest terms
Sometimes written ‰
62.5% as a fraction…
percent ÷ 100 = decimal = numerator ÷ denominator
62.5 ÷ 100 = 0.625
0.625 = 5/8 in lowest terms
5/8
Formula — written step by step
62.5% as a fraction…
percent ÷ 100 = decimal = numerator ÷ denominator
62.5 ÷ 100 = 0.625
0.625 = 625/1000
Divide both by 125
5/8
Per cent means "per hundred", so a percentage is already a fraction with 100 underneath. Reducing it to lowest terms is just dividing top and bottom by their greatest common divisor.
A worked example
A percentage that never terminates
- Fraction
- 1/3
- As a decimal
- 0.333333…
- 1 ÷ 3 = 0.3333333…
- × 100 = 33.3333…%
- Written exactly: 33⅓%
- Rounded to 33.33% loses precision
33.333…% — the decimal never ends
One third has no exact decimal or percentage, because 3 does not divide any power of ten. This is why financial and engineering work keeps fractions in fraction form until the final step: converting early and rounding introduces an error that then compounds.
How to use this calculator
- Choose whether you are starting from a percentage, a fraction or a decimal.
- Enter the value. All three forms are shown together, so the conversion runs in every direction.
- The fraction is always reduced to lowest terms; a mixed number is shown when it is top-heavy.
- Where the decimal does not terminate, the calculator says so and gives the closest simple fraction rather than pretending it is exact.
Three notations, one number
A percentage, a decimal and a fraction are three ways of writing the same quantity. Per cent means "per hundred", so 62.5% is 62.5/100, which is 0.625, which reduces to 5/8. Nothing changes but the notation.
Each form suits a different job. Percentages compare things on a common scale and communicate well. Decimals are what calculators and spreadsheets work in. Fractions are exact, which matters when a value would otherwise be rounded at every step.
Which decimals terminate
A fraction has a terminating decimal only when its denominator, in lowest terms, has no prime factors other than 2 and 5 — the primes that divide ten. That is why halves, quarters, eighths, fifths and tenths all terminate.
Thirds, sixths, sevenths and ninths do not. One third is 0.333… forever, and no amount of decimal places makes it exact. Writing 33.33% instead of 33⅓% introduces a small error, which is fine for a headline and not fine inside a calculation that repeats.
Going backwards from a decimal
Turning a decimal into a fraction is easy when it terminates: write the digits over the matching power of ten and reduce. 0.625 is 625/1000, and dividing both by 125 gives 5/8.
A non-terminating decimal has no exact fraction of that form, so this calculator finds the closest simple one using continued fractions — the same method that produces 22/7 for π. It reports when the result is an approximation rather than presenting it as exact, which a converter that silently rounds cannot do.
Conversions worth knowing by sight
| Fraction | Decimal | Percent | Fraction | Decimal | Percent |
|---|---|---|---|---|---|
| 1/2 | 0.5 | 50% | 1/3 | 0.333… | 33.33% |
| 1/4 | 0.25 | 25% | 2/3 | 0.666… | 66.67% |
| 3/4 | 0.75 | 75% | 1/6 | 0.1666… | 16.67% |
| 1/5 | 0.2 | 20% | 1/8 | 0.125 | 12.5% |
| 2/5 | 0.4 | 40% | 3/8 | 0.375 | 37.5% |
| 1/10 | 0.1 | 10% | 5/8 | 0.625 | 62.5% |
| 1/20 | 0.05 | 5% | 7/8 | 0.875 | 87.5% |
The eighths all terminate because 8 is a power of two, and 2 divides 10. Thirds and sixths never do, because 3 divides no power of ten.
Frequently asked questions
How do I turn a percentage into a fraction?
Put it over 100 and reduce. 62.5% is 62.5/100, which becomes 625/1000, which reduces to 5/8.
Why does 1/3 not give an exact percentage?
Because 3 divides no power of ten, so the decimal repeats forever. The exact value is 33⅓%; 33.33% is a rounding.
What is a mixed number?
A whole number beside a proper fraction, such as 1 ½ for 3/2. It is shown whenever the fraction is top-heavy.
Can a percentage be over 100?
Yes. 150% is 1.5, or 3/2. Percentages above 100 simply mean more than the whole.