Fraction to Decimal Calculator
Convert a fraction or mixed number to a decimal, showing exactly which digits repeat.
About the Fraction to Decimal Calculator
Divide the numerator by the denominator. If the denominator, in lowest terms, has no prime factors other than 2 and 5, the decimal ends; otherwise it repeats, and the calculator finds the repeating block by long division.
The formula
a/b = a ÷ b
- 0.(142857)
- the block 142857 repeats forever
Common fractions as decimals
| Fraction | Decimal |
|---|---|
| 1/2 | 0.5 |
| 1/3 | 0.(3) |
| 1/4 | 0.25 |
| 1/5 | 0.2 |
| 1/6 | 0.1(6) |
| 1/7 | 0.(142857) |
| 1/8 | 0.125 |
| 1/9 | 0.(1) |
| 1/11 | 0.(09) |
| 1/12 | 0.08(3) |
Worked example
Example: 3/8 = 0.375
- Input: Fraction: 3/8.
- Formula: a/b = a ÷ b
- Make the denominator a power of ten: 3/8 = (3 × 125)/(8 × 125) = 375/1000
- Read off the decimal: 375/1000 = 0.375
- Result: 3/8 = 0.375
- Rounded to 4 places: 0.375
- Percentage: 37.5%
- Repeating block: none (terminates)
Questions people ask
Why does 1/7 repeat six digits?
When dividing by 7 there are only six possible non-zero remainders, so the pattern must repeat within six steps.
Which fractions terminate?
Those whose simplified denominator only has 2s and 5s as prime factors.