Fraction to decimal converter
Enter a fraction or mixed number. You get the exact decimal (with the repeating part marked), the percent, and the long division that produced it.
The digits under the line repeat forever (1-digit cycle). The remainder 2 came back, so the division loops.
Long division, one digit at a time
5 ÷ 6: bring down a zero, see how many 6s fit, carry the remainder. When a remainder you've seen before comes back, the digits must repeat from there.
| Divide | Digit | Remainder |
|---|---|---|
| 5 ÷ 6 | 0. | 5 |
| 50 ÷ 6 | 8 | 2 |
| 20 ÷ 6 | 3 | 2 |
How to change a fraction into a decimal
A fraction bar means "divided by". 7/8 is 7 ÷ 8. On a calculator that's the whole job; by hand, long division gives 0.875.
Some fractions are easier with a shortcut: if you can scale the denominator to 10, 100 or 1000, just read off the digits. 3/4 = 75/100 = 0.75, and 7/20 = 35/100 = 0.35.
Terminating or repeating?
Simplify first, then factor the denominator. Only 2s and 5s → the decimal ends (1/8, 3/40, 7/25). Anything else → it repeats (1/3, 5/6, 2/7). This works because 10 = 2 × 5.
Every common fraction (halves to sixteenths, plus 20ths, 25ths, 32nds and 64ths) has its own page in the fraction lookup, e.g. 3/8, 2/3, 13/16.
See the fraction–decimal chart for common values, or go the other way with the decimal to fraction converter.
Questions people ask
How do you convert a fraction to a decimal?
Divide the numerator by the denominator. 3/8 = 3 ÷ 8 = 0.375. With long division, add a decimal point and zeros to the numerator and keep dividing until the remainder is 0 or a remainder repeats.
Why do some fractions give repeating decimals?
In simplest form, a fraction terminates only if its denominator has no prime factors other than 2 and 5 (the factors of 10). Any other factor, like 3 or 7, makes the digits repeat: 1/3 = 0.333…, 1/7 = 0.142857142857…
What is 5/8 as a decimal?
5 ÷ 8 = 0.625.
What is 2/3 as a decimal?
0.6666…, written 0.6 with a bar over the 6, and usually rounded to 0.667.
How long can the repeating part be?
For a denominator d, the repeating block has at most d − 1 digits. 1/7 repeats every 6 digits and 1/17 every 16.