How it works
The percentage is placed over 100 (since "percent" means "per hundred"), then both sides are reduced by their greatest common divisor. A percentage with decimal places, such as 12.5%, is scaled up first so the conversion stays exact.
Worked through once: 87.5% has one decimal place, so it is scaled up by a factor of 10 to give 875/1000. The greatest common divisor of 875 and 1000 is 125, and dividing both by 125 leaves 7/8. That fraction is then an ordinary number in any calculation: seven eighths of 720 is (7 × 720) / 8 = 5040 / 8 = 630.
A decimal such as 0.875 converts the same way on the decimal to fraction calculator. The reverse conversion, 7/8 to 87.5%, is on the fraction to percentage calculator. The guide to fractions, decimals and percentages explains why the three forms are interchangeable and when only one of them is exact.
Formula: Fraction = percentage / 100, then simplified.
Examples
A whole-number percentage
25% = 25/100, which simplifies to 1/4.
A decimal percentage
12.5% = 125/1000, which simplifies to 1/8.
A percentage that came from a fraction
87.5% is 7/8, because 7 / 8 = 0.875 and 0.875 × 100 = 87.5. Seven eighths of 720 is (7 × 720) / 8 = 5040 / 8 = 630, so 87.5% of 720 is 630, and the same percentage of 880 is (7 × 880) / 8 = 770.
A percentage that has been rounded
76.92% is 7692/10000, which reduces to 1923/2500 and cannot be reduced further, because 76.92 is exactly the number entered. The tidier answer is usually the fraction it was rounded from: 10/13 = 76.9230769...%, so if that is the origin, write 10/13 rather than 1923/2500.
Common uses
- Checking a test score written as a percentage before rewriting it as a fraction for an answer
- Expressing a proportion such as 87.5% as 7/8 so it can be multiplied by a quantity exactly
- Comparing a percentage discount with the equivalent fraction, for example when checking a price cut against the discount calculator
Things to keep in mind
- A negative percentage converts to a fraction with a negative numerator, such as −50% to −1/2.
- The number entered is the number converted. 76.92% becomes 1923/2500 rather than a tidier fraction such as 10/13, which is a consequence of the rounding that produced 76.92%, not an error in the conversion.
- The result is exact, never rounded: the numerator and denominator are whole numbers. The rounding used for decimal and percentage outputs elsewhere on this site does not apply to a fraction.
- A percentage entered with too many decimal places to scale up into a whole number exactly is rejected rather than rounded.