The basic method: divide, then multiply by 100
To change a fraction to a percent, divide the top number (numerator) by the bottom number (denominator), then multiply the result by 100. That's it. The number you get is your percentage.
Here's a concrete example: the fraction 3/4. Divide 3 by 4, which gives you 0.75. Multiply 0.75 by 100, and you get 75%. So 3/4 = 75%.
You can do this division on any calculator, or by hand if you remember long division. The multiplication by 100 is just moving the decimal point two places to the right.
Key Takeaways
- Divide the numerator (top number) by the denominator (bottom number) to get a decimal.
- Multiply that decimal by 100 to turn it into a percentage.
- If your decimal doesn't divide evenly, round to a sensible number of decimal places before multiplying by 100.
- You can check your work by converting the percentage back to a fraction and seeing if it matches the original.
- Percentages larger than 100% are normal and occur whenever you have more than one whole unit.
Working with fractions that don't divide evenly
Some fractions don't give you a clean decimal. Take 1/3: when you divide 1 by 3, you get 0.333333... repeating forever. Multiply that by 100 and you get 33.333...%.
In real life, you round. For most purposes, 33.33% or even 33% is close enough. If you're working on homework or a test, your teacher will tell you how many decimal places to keep. If nobody tells you, two decimal places (33.33%) is standard.
Another example: 5/6. Divide 5 by 6 to get 0.8333... Rounded to two decimal places, that's 0.83, which becomes 83.33%. The rounding happens before you multiply by 100, so you don't end up with too many digits in your final answer.
Fractions larger than 1 (improper fractions)
If your fraction is larger than 1 — like 5/4 or 7/3 — the same method works, and your percentage will be larger than 100%.
With 5/4: divide 5 by 4 to get 1.25. Multiply by 100 to get 125%. This makes sense: 5/4 is one whole thing plus a quarter, so it's more than 100%.
Don't let percentages over 100% throw you. They're perfectly normal and show up whenever you have more than one whole unit. You might see them in contexts like "sales increased by 150%" or "the recipe calls for 200% of the original amount".
Converting percentages back to fractions to check your work
If you want to make sure you did the math right, reverse the process. Take your percentage, divide by 100, and see if you can simplify it back to your original fraction.
Say you converted 3/4 and got 75%. Divide 75 by 100 to get 0.75, which is 75/100. Now simplify: both 75 and 100 are divisible by 25, so 75/100 becomes 3/4. You're back where you started, so your conversion was correct.
This check works even with repeating decimals. If you converted 1/3 to 33.33%, divide 33.33 by 100 to get 0.3333, which is very close to 1/3. The tiny difference is just from rounding, not from an error in your method.
Using a shortcut with fractions that have 100 as the denominator
If your fraction already has 100 in the denominator, you can skip the division step. The numerator is already your percentage. For example, 45/100 is just 45%.
This is why percentages are called "per cent" — they literally mean "per 100". If you can rewrite your fraction with 100 on the bottom, the top number is your answer.
Example: 1/4. You know that 1/4 = 25/100, so it's 25%. Or 3/5 = 60/100, so it's 60%. This method is faster if you can do the conversion in your head, and it's especially useful when you're working with money (which is already divided into 100 cents).
Common fractions and their percentages
Some fractions come up so often that it's worth memorizing their percentages. Once you know these, you can estimate percentages for fractions close to them.
| Fraction | Percentage |
| 1/2 | 50% |
| 1/4 | 25% |
| 3/4 | 75% |
| 1/3 | 33.33% |
| 2/3 | 66.67% |
| 1/5 | 20% |
| 2/5 | 40% |
| 1/10 | 10% |
If you see a fraction like 7/20 and you're not sure, you can think: 1/5 is 20%, so 2/5 is 40%, so 7/20 should be somewhere between 30% and 40%. (The exact answer is 35%.) This estimation skill is useful when you need a quick answer and don't have a calculator nearby.
Frequently Asked Questions
What if I get a decimal with lots of digits after the decimal point?
Round to two decimal places before multiplying by 100. So if your division gives you 0.666666..., round to 0.67, then multiply by 100 to get 67%. If your teacher or assignment asks for more precision, they'll tell you how many decimal places to keep.
Do I always have to multiply by 100, or can I just move the decimal point?
Moving the decimal point two places to the right is the same as multiplying by 100. So if you have 0.75, moving the decimal right twice gives you 75. Both methods work; use whichever feels easier to you.
What if the fraction is already a percentage, like 50/100?
The numerator is your percentage. 50/100 = 50%. You don't need to divide or multiply; the denominator tells you it's already "per 100".
Can a percentage be a decimal, like 33.33%?
Yes. Percentages can have decimal places. 33.33% is a valid way to write the percentage for 1/3. Most of the time you'll round to one or two decimal places, but more precision is fine if you need it.
What's the difference between a percentage and a decimal?
A decimal and a percentage represent the same number, just written differently. The decimal 0.75 and the percentage 75% are the same value. Percentages are often easier to understand because people think in terms of "out of 100" more naturally than decimals.