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Percent to Fraction Calculator
To turn a percent into a fraction, write it over 100 and reduce. 45% is 45/100, and dividing both by 5 gives 9/20. For a decimal percent, clear the decimal first: 37.5% is 375/1000, which reduces to 3/8. 33 1/3% is exactly 1/3, but 33% is 33/100. This calculator shows each step.
Over 100, then reduce.
- Write it over 100: 37.5/100.
- Clear the decimal: multiply the top and bottom by 10, giving 375/1000.
- The greatest common divisor of 375 and 1000 is 125, so divide both by it: 3/8.
| Result | Value |
|---|---|
| Fraction (lowest terms) | 3/8 |
| Decimal | 0.375 |
| Over 100 | 37.5/100 |
The figure above is an example: put in your own, with or without the % sign. Decimal percents (12.5), fractional ones (33 1/3 or 1/2) and repeating ones in brackets (33.(3)) are all converted exactly. Worked out exactly in this browser and kept there; nothing is sent anywhere.
Type a percent and read it as a fraction in lowest terms, and as a mixed number when it is over 100%. Decimal, fractional and repeating percents are converted exactly, step by step.
Converting a percent to a fraction writes it as a number over 100 and then simplifies: 45% is 45/100, which is 9/20 in lowest terms.
- No sign-up
- Nothing uploaded
- Shows every step
- Works offline
- Exact, no rounding errors
Key facts
| Detail | Answer |
|---|---|
| Rule | Over 100, clear the decimal, divide by the greatest common divisor |
| Example | 37.5% = 375/1000 = 3/8 |
| Over 100% | 150% = 3/2 = 1 1/2 |
| Exact thirds | 33 1/3% = 33.(3)% = 1/3; 33% = 33/100 |
| Accepts | 45, 45%, 37.5, 0,5, 33 1/3, 33.(3), 1/2 |
| Where your numbers are kept | This browser only |
How to convert a percent to a fraction
Over 100, clear the decimal, reduce.
Write it over 100
45% becomes 45/100.
Clear any decimal
37.5/100: multiply top and bottom by 10 to get 375/1000.
Find the greatest common divisor
For 375 and 1000 it is 125.
Divide top and bottom by it
375/1000 becomes 3/8.
Make a mixed number if over 100%
150% is 3/2, which is 1 1/2.
Who converts percents to fractions
Anyone who finds a fraction easier to picture or to work with.
Students
Percent to fraction in simplest form, with the steps.
Cooks
75% of a cup is 3/4 of a cup.
Shoppers
12.5% off is an eighth off the price.
Woodworkers
A percentage of an inch as a ruler fraction.
Teachers
Worked examples for any percent.
Readers of odds
20% as 1 in 5.
Percent to fraction: over 100, clear the decimal, reduce
Every percent is already a fraction: a number over 100. The work is in clearing any decimal and then reducing. The calculator names each step, in this order.
| Step | 37.5% | 45% |
|---|---|---|
| 1. Write it over 100 | 37.5% = 37.5/100 | 45% = 45/100 |
| 2. Clear the decimal | × 10 top and bottom: 375/1000 | No decimal: skip |
| 3. Find the greatest common divisor | GCD(375, 1000) = 125 | GCD(45, 100) = 5 |
| 4. Divide both by it | 375/1000 = 3/8 | 45/100 = 9/20 |
| 5. Over 100%? Make a mixed number | Not needed | Not needed |
A percent with a fraction in it, such as 33 1/3%, divides the fraction by 100 directly: 33 1/3 is 100/3, and 100/3 ÷ 100 = 1/3. A percent written as a repeating decimal, 33.(3)%, is first turned into its fraction by the subtraction method the Common Core sets for Grade 8 (8.NS.A.1: convert a repeating decimal into a rational number), then divided by 100. Both give exactly 1/3, which 33% and 33.33% do not.
Common percents as fractions
Some percents are worth knowing as fractions because they turn mental arithmetic into one division. 12.5% off is an eighth off; 66 2/3% is two thirds.
| Percent | Fraction | Percent | Fraction |
|---|---|---|---|
| 10% | 1/10 | 20% | 1/5 |
| 12.5% | 1/8 | 25% | 1/4 |
| 16 2/3% | 1/6 | 33 1/3% | 1/3 |
| 37.5% | 3/8 | 40% | 2/5 |
| 62.5% | 5/8 | 66 2/3% | 2/3 |
| 75% | 3/4 | 83 1/3% | 5/6 |
| 87.5% | 7/8 | 150% | 3/2 = 1 1/2 |
| 0.5% | 1/200 | 2.5% | 1/40 |
The two columns are a percent table read either way: 1/8 of 240 is 30, so 12.5% of 240 is 30. The same trick in reverse is the fraction to percent calculator.
33% is not 1/3: rounded percents and close fractions
Rounded percents are not the fractions they look like. 33% is 33/100, not 1/3, and 67% is 67/100, not 2/3. The difference is small, but it shows up the moment the percent is used on a large number or compared with an exact share. When the fraction you get has a large denominator, the calculator says which simple fraction it is close to, and that it is not equal.
| Percent | Exact fraction | Close simple fraction | Gap |
|---|---|---|---|
| 33% | 33/100 | 1/3 = 33.(3)% | 0.(3) points |
| 67% | 67/100 | 2/3 = 66.(6)% | 0.(3) points |
| 17% | 17/100 | 1/6 = 16.(6)% | 0.(3) points |
| 14% | 7/50 | 1/7 = 14.(285714)% | 0.29 points |
| 12% | 3/25 | 1/8 = 12.5% | 0.5 points |
| 88% | 22/25 | 7/8 = 87.5% | 0.5 points |
Which to use depends on where the percent came from. A poll result of 33% is 33/100 of those asked; a recipe that says “about a third” and a sign that says 33% are describing 1/3 and rounding it. If the source rounded, the exact fraction of the printed percent is not more accurate than the simple one.
What this calculator does not do
The calculator converts one percent to one fraction. It reduces to lowest terms with the greatest common divisor and gives a mixed number when the percent is over 100%. It does not guess what a rounded percent “really” meant: 33% gives 33/100, with 1/3 offered only as a close fraction. Negative percents give negative fractions. For the arithmetic of fractions, adding or dividing them, use the fraction calculator; to see a fraction’s decimal, the fraction to decimal calculator.
This calculator or an answer-only one
What this page does that a typical answer-only widget does not.
| This page | A typical calculator | |
|---|---|---|
| Fractional percents | 33 1/3% gives 1/3 | Decimals only |
| Repeating percents | 33.(3)% accepted | Not accepted |
| Close fractions | 33% is near 1/3, not equal: said | Not mentioned |
| Shows the steps | Over 100, clear, reduce | Answer only |
| Exact arithmetic | Whole numbers only | Floating point |
| Your numbers leave the browser | Never | Varies |
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Frequently asked questions
How do you convert a percent to a fraction?
Write the percent over 100 and simplify. 45% is 45/100; the greatest common divisor of 45 and 100 is 5, so it reduces to 9/20. If the fraction is more than 1, write it as a mixed number: 150% is 150/100 = 3/2 = 1 1/2.
How do you convert a decimal percent like 37.5% to a fraction?
Write it over 100, then multiply top and bottom by 10 for each decimal place to clear it: 37.5/100 becomes 375/1000. Reduce by the greatest common divisor, 125, to get 3/8. 12.5% is 1/8 and 62.5% is 5/8 the same way.
Is 33% equal to 1/3?
No. 33% is 33/100, while 1/3 is 33.(3)%, with the 3 repeating. The gap is a third of a percentage point. 33 1/3% is exactly 1/3. When a percent has been rounded, the simple fraction may be what was meant, but the printed percent is not equal to it.
What is 66 2/3% as a fraction?
2/3. 66 2/3 is 200/3, and dividing by 100 gives 200/300, which reduces to 2/3. Likewise 16 2/3% is 1/6 and 83 1/3% is 5/6. Type these in the calculator with a space between the whole number and the fraction.
How do you write a percent over 100 as a fraction?
The same way, and the fraction will be more than 1. 125% is 125/100 = 5/4 = 1 1/4; 250% is 5/2 = 2 1/2. A mixed number makes the size easier to see: 1 1/4 is the whole plus a quarter more.
What is 0.5% as a fraction?
1/200. 0.5/100 becomes 5/1000 after clearing the decimal, and dividing both by 5 gives 1/200. Small percents give large denominators: 0.1% is 1/1000 and 2.5% is 1/40. A percent below 1% always gives a fraction smaller than 1/100, and the calculator reduces each one to lowest terms with the greatest common divisor named.
What does simplest form mean?
A fraction is in simplest form, or lowest terms, when the top and bottom have no common factor except 1. Dividing both by their greatest common divisor gets there in one step. The calculator names that divisor in its working.
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