Quick start
- Type a fraction (7/16), a mixed number (2 3/5) or a negative fraction (-3/8).
- Read the decimal and the percent.
- Follow the long division steps, with the repeating part marked if there is one.
Fraction to decimal in one move
A fraction is a division. 7/16 means 7 ÷ 16 = 0.4375. To get a percent, multiply by 100: 43.75%.
Will the decimal end or repeat?
Simplify the fraction first, then look at the prime factors of the bottom number. If they are only 2s and 5s, the decimal ends: 7/16 has 16 = 2⁴, so it ends. If any other prime appears, the decimal repeats: 5/12 has 12 = 2² × 3, so it gives 0.41666…
How repeats are detected
In long division, each step leaves a remainder smaller than the divisor. There are only so many possible remainders, so one must eventually come back. When a remainder repeats, the digits after it repeat too. The tool records every remainder to find exactly where the cycle starts.
Handy conversions
| Fraction | Decimal | Percent |
|---|---|---|
| 1/6 | 0.1666… | 16.67% |
| 1/7 | 0.142857… | 14.29% |
| 3/16 | 0.1875 | 18.75% |
| 2/5 | 0.4 | 40% |
| 5/12 | 0.41666… | 41.67% |
| 9/20 | 0.45 | 45% |
| 11/16 | 0.6875 | 68.75% |
| 4/9 | 0.444… | 44.44% |
Common questions
What is 5/7 as a decimal?
0.714285714285…, where the six digits 714285 repeat. As a percent it is about 71.43%.
How long can the repeating block be?
For a denominator n, the block has at most n − 1 digits. 1/7 repeats every 6 digits; 1/17 every 16.
Can I go from a decimal back to a fraction?
Yes, with the Decimal to Fraction Calculator.