About the Percent to Fraction Converter
This percent to fraction converter turns a percentage such as 37.5% into its simplest fraction (3/8), a mixed number when it is over 100%, and its decimal form, showing the divide-by-100 and simplify steps. Switch the direction to convert a fraction like 2/3 or a decimal like 0.045 into a percentage instead.
It is handy for students practising fraction–decimal–percent conversions, for reading discounts and statistics ("12.5% off" is one-eighth), and for recipes, test scores and survey results where a fraction is easier to picture than a percent. Inputs can be whole numbers, decimals, fractions or mixed numbers, so 33 1/3% converts exactly to 1/3.
All arithmetic uses exact fractions, so there is no rounding in the fraction result; percentages that repeat forever, such as 2/3 = 66.666…%, are also shown in exact mixed form (66 2/3%).
How to use the percent to fraction converter
- 1Choose the direction: percent to fraction, fraction to percent, or decimal to percent.
- 2Type the value — e.g. 37.5, 33 1/3, 5/8 or 0.045.
- 3Read the simplified fraction, decimal and percent.
- 4Check the unsimplified fraction and GCD to see how it was reduced.
Formula and method
A percent is a fraction with denominator 100, so p% = p/100. If p has decimals, multiply top and bottom by a power of 10 to clear them (37.5/100 = 375/1000), then divide both by their greatest common divisor to reach lowest terms (375/1000 ÷ 125 = 3/8).
Going the other way, divide the numerator by the denominator to get a decimal and multiply by 100 to get the percent; a decimal becomes a percent by moving the decimal point two places to the right. When the denominator has prime factors other than 2 and 5, the decimal repeats, so the exact percent is shown as a mixed number such as 66 2/3%.
- p
- Percentage value
- a/b
- Fraction (numerator / denominator)
- GCD
- Greatest common divisor used to simplify
Worked examples
37.5% as a fraction
37.5% = 37.5/100. Multiply top and bottom by 10 to get 375/1000, then divide both by their GCD, 125, to get 3/8 = 0.375.
125% as a mixed number
125% = 125/100 = 5/4 after dividing by 25. Because it is over 100% the fraction is improper; as a mixed number it is 1 1/4.
33 1/3% exactly
33 1/3 = 100/3, and (100/3)/100 = 1/3. Typing it as a mixed number keeps the answer exact instead of 0.3333.
Fraction 2/3 to percent
2 ÷ 3 = 0.6666…, and × 100 gives 66.666…%, which rounds to 66.6667%. Exactly, it is 66 2/3%.
Decimal 0.045 to percent
Moving the decimal point two places right turns 0.045 into 4.5%. As a fraction, 45/1000 simplifies (÷5) to 9/200.
Frequently asked questions
How do you convert a percent to a fraction?+
Write the percent over 100 and simplify. For example 60% = 60/100; dividing top and bottom by 20 gives 3/5. If the percent has decimals, multiply top and bottom by 10 or 100 first to make them whole numbers.
How do you convert a fraction to a percent?+
Divide the numerator by the denominator and multiply by 100. For 3/8: 3 ÷ 8 = 0.375, and 0.375 × 100 = 37.5%.
What is 12.5% as a fraction?+
12.5% = 12.5/100 = 125/1000 = 1/8. Other common ones: 25% = 1/4, 20% = 1/5, 33 1/3% = 1/3, 62.5% = 5/8, 75% = 3/4.
How do I write a percent over 100% as a fraction?+
The same way — it just gives an improper fraction. 150% = 150/100 = 3/2, which is 1 1/2 as a mixed number.
How do you convert a decimal to a percent?+
Multiply by 100, which moves the decimal point two places to the right: 0.07 = 7%, 0.425 = 42.5%, 1.2 = 120%.