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

InputUnitRequiredNotes
NumeratornumberYes
DenominatornumberYes

How to use it

  1. Enter Numerator and Denominator.
  2. 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…

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