OneTaskBy Tim King · Updated
Percent to Fraction Calculator
Decimals Like 37.5% and Mixed Forms Like 33 1/3%, Simplified With Working
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How the Percent to Fraction Calculator works
This percent to fraction calculator writes any percentage as a fraction in lowest terms and as a decimal, with each step shown. Decimal percentages such as 37.5%, mixed ones such as 33 1/3%, repeating ones such as 16.(6)%, and values above 100% all work.
Per cent means per hundred, so every percentage is already a fraction with 100 on the bottom. 45% is 45/100. The only work is clearing any decimal point and cancelling down to the simplest form.
How the percent to fraction calculator works
The formula is p% = p/100, then simplify. If p has decimal places, multiply the top and the bottom by 10, 100 or 1000 until the top is whole. If p is a mixed number such as 33 1/3, turn it into an improper fraction first and multiply the denominators together. Finally, divide the top and the bottom by their greatest common factor.
First example. 37.5% = 37.5/100. Multiply both by 10 to get 375/1000. Both divide by 125, so 37.5% is 3/8.
Second example. 33 1/3% = (100/3)/100 = 100/300, which is 1/3.
How many people in a class of 30 is 40%? 40% is 2/5, and 2/5 of 30 is 12 people.
Common percentages as fractions in lowest terms and as decimals
| Percentage | Fraction | Decimal |
|---|---|---|
| 1% | 1/100 | 0.01 |
| 5% | 1/20 | 0.05 |
| 10% | 1/10 | 0.1 |
| 12.5% | 1/8 | 0.125 |
| 20% | 1/5 | 0.2 |
| 25% | 1/4 | 0.25 |
| 33 1/3% | 1/3 | 0.(3) |
| 37.5% | 3/8 | 0.375 |
| 40% | 2/5 | 0.4 |
| 50% | 1/2 | 0.5 |
| 60% | 3/5 | 0.6 |
| 62.5% | 5/8 | 0.625 |
| 66 2/3% | 2/3 | 0.(6) |
| 70% | 7/10 | 0.7 |
| 75% | 3/4 | 0.75 |
| 80% | 4/5 | 0.8 |
| 87.5% | 7/8 | 0.875 |
| 90% | 9/10 | 0.9 |
| 100% | 1 | 1 |
| 125% | 1 1/4 | 1.25 |
| 150% | 1 1/2 | 1.5 |
| 200% | 2 | 2 |
Tips
- Learn the eighths. 12.5%, 37.5%, 62.5% and 87.5% are 1/8, 3/8, 5/8 and 7/8.
- Thirds do not end. 33.3% is close to a third but is really 333/1000. Type 33 1/3 for the exact third.
- Over 100% is fine. 150% is 3/2, or 1 1/2 times the whole.
FAQ
How do you convert a percent to a fraction?
Write the percentage over 100 and simplify. 85% is 85/100; both numbers divide by 5, giving 17/20. If the percentage has a decimal, multiply the top and bottom by 10 for each decimal place first, so 2.5% becomes 25/1000, which is 1/40.
What is 12.5% as a fraction?
12.5% is 12.5/100, which is 125/1000 once the decimal is cleared. Both divide by 125, leaving 1/8. That is why 12.5% off is the same as an eighth off, and why 87.5% is 7/8. Eighths come up often in discounts, recipes and test scores.
How do you write 33 1/3% as a fraction?
Change 33 1/3 into an improper fraction, 100/3, then divide by 100. That gives 100/300, which simplifies to 1/3. In the same way, 66 2/3% is 2/3 and 16 2/3% is 1/6. Type the mixed form with a space, such as 33 1/3, and the calculator handles it.
What is the difference between a percent and a fraction?
They are two ways to write the same amount. A percentage always uses 100 as the bottom number, which makes values easy to compare. A fraction can use any bottom number, which often gives a simpler picture: 75% and 3/4 are equal, but three out of four is easier to imagine.
See also: all Arithmetic tools, Number Theory, Algebra and Geometry, Statistics, Trigonometry and Calculus.
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