How to solve it
- Divide the numerator by the denominator.
- Multiply the result by 100.
- Add the % sign.
- To go back, write the percentage over 100 and simplify.
3/20 × 100 = 300/20 = 15
3/20 = 15%
Result: 15%
Common mistake:Wrong: 1/4 = 4%.Right: 1/4 = 25%.The bottom number is not the percentage. A quarter of 100 is 25, so 1/4 = 25%.
Percent means parts out of every 100, so the percent of a fraction tells you how many parts out of 100 it represents. The calculator above multiplies by 100 using exact fractions, reduces the result, and shows it with the number of decimal places you choose. If you are starting from a percent, use percent to fraction.
A tank filled to 7/8
A water tank is filled to 7/8 of its capacity. What percent is full?
- Multiply by 100. 7/8 × 100 = 700/8.
- Simplify. 700 and 8 are both divisible by 4, so 700/8 = 175/2.
- Convert to a decimal. 175 ÷ 2 = 87.5.
So 7/8 = 87.5%.
Check. Going back, 87.5/100 = 0.875, and 7 ÷ 8 is also 0.875. Also, 87.5% falls between 75% (which is 3/4) and 100%, as it should for a fraction a little less than 1.
How multiplying by 100 works
A percent is a fraction with a denominator of 100. Writing 87.5% means 87.5 out of every 100, that is, 87.5/100. So to convert a/b, you look for the number x such that a/b = x/100. Solving for x gives x = 100 × a/b, which is the rule above.
When the denominator divides 100, there is a shortcut: build the fraction up to an equivalent fraction with a denominator of 100, and the numerator is already the percent. With 3/20, since 20 × 5 = 100, you get 15/100 = 15%. When the denominator does not divide 100, as with 8, it is easier to multiply and divide. For more examples of building up and simplifying, see equivalent fractions.
Cases that change the result
The table collects five cases that change how the result looks. The same rule applies in all of them; only the look of the result changes.
| Case | Calculation | Percent |
|---|---|---|
| Proper fraction with a terminating decimal | 1/8 × 100 = 100/8 | 12.5% |
| Denominator that divides 100 | 7/20 = 35/100 | 35% |
| Fraction greater than 1 | 5/4 × 100 = 500/4 | 125% |
| Mixed number | 1 1/2 = 3/2, and 3/2 × 100 | 150% |
| Negative fraction | −1/4 × 100 | −25% |
If the number is mixed, each whole contributes 100% and the fraction part adds its own percent: 1 1/2 is 100% plus 50%. A negative fraction keeps its sign, and a decimal such as 0.375 gives the same result as 3/8: 37.5%. To see how fractions and decimals relate, the fraction to decimal page works through that middle step.
When the percent does not terminate
With denominators such as 3, 6, 7, or 9, the percent has infinitely many decimal places. For 1/3, 100/3 = 33 1/3, and as a decimal it is 33.333… With four decimal places, the screen shows 33.3333, which is a rounded value and so carries the “Approximate” label. The full value, 100/3%, appears in the expression line and is the one used if you chain another operation.
When rounding lands exactly halfway, it goes to the value farther from zero. With zero decimal places, 37.5% displays as 38%. The percents for the most common fractions are collected in the fraction, decimal, and percent table, with the repeating block marked where there is one.
When to use a different page
This page starts from a fraction you already have. If you have a percent, percent to fraction goes the other way. If you have two amounts, such as 12 out of 80, what fraction is one number of another finds the fraction and the percent in one step. And to find a percent of an amount, a discount, or an increase, there is the percentage calculator.
Some countries write the decimal with a comma, so you may see 87,5% instead of 87.5%; the calculator understands both forms. The “Understand Percent” section of OpenStax Prealgebra 2e, 6.1 defines a percent as a ratio with a denominator of 100 (accessed October 16, 2026).
Frequently asked questions
Why can a percent be more than 100%?
Because the fraction is greater than 1, so there is more than one whole of reference. With 9/5 = 1.8 wholes, the percent is 180%. It happens when you compare an amount with a smaller base, for example when something nearly doubles. A percent above 100 is not an error.
How do you write 1/6 as a percent, exact and rounded?
The full value is 100/6%, which reduces to 50/3% and is written 16 2/3%. As a decimal it is 16.666…%, so 16.67% is an approximation to two decimal places. Use the full value if you will keep calculating, and the rounded one only for display.
How many decimal places should I show?
As many as the context calls for. For a grade or a split, 0 or 1 decimal places are enough; for a results table, 2. With 2/7 the percent is 200/7%, and it shows as 29% with zero decimal places, 28.6% with one, and 28.57% with two. The displayed figure changes, but the value does not.
How do I turn a percent into a fraction?
It is the reverse path: divide by 100 and simplify. So 45% = 45/100 = 9/20. For decimals such as 12.5%, first multiply the top and bottom by 10 to get 125/1000 = 1/8. The percent to fraction page shows every step.