Converting Between Fractions, Decimals and Percentages
Three-eighths, 0.375 and 37.5% all describe exactly the same amount. Which form is best depends on the job: fractions suit exact parts, decimals suit calculators and measurement, and percentages suit comparisons. Being able to move between them quickly makes a lot of everyday maths easier.
This guide gives the rule for each conversion with a worked example, explains why some fractions give endless decimals, and ends with a table of equivalents that are worth knowing by heart.
From fraction to decimal to percent
A fraction is a division in disguise. To get the decimal, divide the top number (numerator) by the bottom number (denominator). To get the percent, multiply that decimal by 100.
fraction a/b → decimal = a ÷ b → percent = (a ÷ b) × 100
Worked example: convert 3/8. Divide 3 by 8 to get 0.375. Multiply by 100 to get 37.5%. For a mixed number such as 1 3/4, convert the fraction part (3/4 = 0.75) and keep the whole number, giving 1.75, which is 175%.
From percent to decimal to fraction
Going the other way reverses each step. Divide the percent by 100 (move the decimal point two places left) to get the decimal. To make a fraction, write the percent over 100 and simplify.
Worked example: convert 62.5% to a fraction. As a decimal it is 0.625. Write it over 1,000: 625/1000. The greatest common divisor of 625 and 1,000 is 125, so dividing both by 125 gives 5/8. Check: 5 ÷ 8 = 0.625.
The same method turns any terminating decimal into a fraction. Count the digits after the decimal point, use that many zeros in the denominator, then simplify. So 0.375 = 375/1000 = 3/8, and 0.04 = 4/100 = 1/25.
Why some fractions never end
Dividing 1 by 3 never finishes: 0.3333… repeats forever. A fraction in lowest terms gives a terminating decimal only if its denominator has no prime factors other than 2 and 5. So 1/8 (2 × 2 × 2) and 3/20 (2 × 2 × 5) terminate, while 1/3, 1/6 and 1/7 do not.
You can turn a repeating decimal back into an exact fraction with a short algebra trick. Worked example: let x = 0.272727… The repeating block has two digits, so multiply by 100: 100x = 27.272727… Subtract the first line from the second: 99x = 27. Then x = 27/99, which simplifies to 3/11.
When a decimal repeats, rounding it (0.33 for 1/3) is an approximation. Keep the fraction when you need an exact answer, and round only at the final step.
Equivalents worth memorising
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333… | 33.3% |
| 2/3 | 0.666… | 66.7% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 1/10 | 0.1 | 10% |
| 1/20 | 0.05 | 5% |
Once you know these, many others follow. Three-eighths is three times one-eighth, so 3 × 12.5% = 37.5%. Seven-tenths is simply 0.7, or 70%.
Shortcuts and comparing mixed forms
When the denominator divides evenly into 100, you can skip the long division and scale the fraction to a denominator of 100. Worked example: 7/20. Since 20 × 5 = 100, multiply the top and bottom by 5 to get 35/100, which is 35%. In the same way, 3/25 = 12/100 = 12%.
To compare numbers written in different forms, convert them all to decimals. Worked example: which is larger, 5/8 or 0.62? Since 5/8 = 0.625 and 0.62 is slightly smaller, 5/8 is larger. A third value, 61%, equals 0.61, so the order from largest to smallest is 5/8, 0.62, 61%.
For a fraction like 7/12, long division gives 0.58333…, so the percentage is about 58.3%. Round only at the end, and say how many places you kept, because 58%, 58.3% and 58.33% are progressively closer approximations of the same exact value.
Choosing the right form
- Fractions keep things exact, especially with thirds, sixths and sevenths, and are natural for measurements such as 3/8 of an inch.
- Decimals are best for calculators, spreadsheets and money, where values line up by place value.
- Percentages make quick comparisons easy. Saying 18/24 and 21/28 are both 75% shows at once that they are equal.
To check a conversion, use the fraction to decimal calculator or work backwards with the decimal to fraction calculator. If you start from a percentage, the percent to fraction calculator shows the simplified result.
- Fraction to Decimal Calculator: Enter the top and bottom of a fraction and the calculator divides them for you. The guide explains how the conversion works, why some fractions repeat forever and lists the decimals you will meet most often.
- Decimal to Fraction Calculator: Type a decimal and get the matching fraction in lowest terms, plus the mixed-number form when the value is above 1.
- Percent to Fraction Calculator: Enter a percentage to see it written as a fraction in lowest terms, or as a mixed number when it is above 100%. The guide below shows how to do the conversion by hand and lists the fractions you will meet most often.
This article is general information, not professional advice. See our Disclaimer and Editorial Policy.
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