Fractions and decimals are two ways to write the same number
A fraction such as 3/8 and the decimal 0.375 describe exactly the same amount. Recipes, measurements in inches, and many school problems use fractions, while calculators, money and spreadsheets use decimals. This converter switches between the two in either direction, simplifies fractions to lowest terms, and shows repeating decimals exactly instead of rounding them.
How to use the converter
- Fraction to decimal: enter the numerator (top) and denominator (bottom). For a mixed number like 2 3/4, also enter the whole number.
- Decimal to fraction: type a decimal. For a repeating decimal, put the repeating part in brackets: 0.(3) means 0.3333…
- Read the result, the simplified form and the percentage.
Fraction to decimal: long division
Divide the numerator by the denominator. 5 ÷ 12 = 0.41666…, where the 6 repeats forever, so the tool writes 0.41(6). A fraction gives a terminating decimal only when its denominator (in lowest terms) has no prime factors other than 2 and 5. That is why 3/8 = 0.375 ends, but 1/3 and 5/12 repeat.
Decimal to fraction
For a terminating decimal, write the digits over a power of 10 and simplify:
0.375 = 375/1000 = (375 ÷ 125)/(1000 ÷ 125) = 3/8
For a repeating decimal, algebra removes the endless part. For x = 0.(36): 100x = 36.(36), so 100x − x = 36, giving x = 36/99 = 4/11. The tool uses this method for any repeating pattern.
Common conversions
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.(3) | 33.33% |
| 1/4 | 0.25 | 25% |
| 1/8 | 0.125 | 12.5% |
| 2/3 | 0.(6) | 66.67% |
| 1/7 | 0.(142857) | 14.29% |
Frequently asked questions
How do I simplify a fraction?
Divide the top and bottom by their greatest common divisor. Our GCD and LCM Calculator finds it with steps.
Why does 0.1 + 0.2 not equal 0.3 on some computers?
Computers store decimals in binary, where 0.1 is a repeating fraction. This tool uses exact whole-number arithmetic for decimal to fraction conversion to avoid that problem.
Can I enter negative numbers?
Yes. Put a minus sign before the decimal or the numerator.