Fraction to Decimal Calculator
Convert any fraction to its decimal form and detect repeating digits.
What the Fraction to Decimal Calculator does
A fraction is just a division waiting to happen: the numerator divided by the denominator. Once reduced, the fraction terminates as a decimal only if its denominator has no prime factors other than 2 and 5.
Formula
Decimal = Numerator ÷ Denominator
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| Numerator | number | Yes | — |
| Denominator | number | Yes | — |
How to use it
- Enter Numerator and Denominator.
- Select Calculate.
Worked example
Convert 7/8 to a decimal.
- Numerator
- 7
- Denominator
- 8
7 ÷ 8 = 0.875, a terminating decimal, or 87.5%.
Reading the result
- A reduced fraction terminates as a decimal only when its denominator has no prime factors beyond 2 and 5. Any other factor produces a repeating decimal.
- The repeating block is at most one digit shorter than the denominator, which is why sevenths cycle through six digits.
Common mistakes
- Dividing the denominator by the numerator. The fraction bar means numerator ÷ denominator, in that order.
- Carrying a truncated decimal into further arithmetic, which compounds the rounding at every step.
Frequently asked questions
Why does 1/3 never finish?
Its denominator contains the prime 3, which does not divide any power of 10, so the long division repeats forever as 0.333…