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Converting Fractions to Decimals (and When They Repeat)

By The Numvella Team · 1 min read

A fraction is really just a division waiting to happen. Converting one to a decimal takes a single step — and a little number theory tells you in advance whether the result will end neatly or repeat forever.

The basic method

Divide the numerator (top) by the denominator (bottom). So 3/4 means 3 ÷ 4 = 0.75, and 7/8 means 7 ÷ 8 = 0.875. That's the whole method — everything else is shortcuts and edge cases.

Common fractions worth memorizing

FractionDecimalPercent
1/20.550%
1/30.333…33.3%
1/40.2525%
1/50.220%
1/80.12512.5%
1/100.110%
3/40.7575%

Terminating vs repeating decimals

Some fractions end (terminate), like 3/4 = 0.75. Others repeat forever, like 1/3 = 0.333… There's a simple rule: reduce the fraction to lowest terms, then look at the denominator. If its only prime factors are 2 and 5, the decimal terminates. If any other prime factor remains (3, 7, 11, …), it repeats.

  • 1/8 → denominator 8 = 2×2×2 → terminates (0.125).
  • 1/20 → denominator 20 = 2×2×5 → terminates (0.05).
  • 1/3 → denominator 3 → repeats (0.333…).
  • 1/6 → denominator 6 = 2×3 → repeats (0.1666…).

Fractions to percentages

Once you have the decimal, multiply by 100 to get a percentage: 3/4 = 0.75 = 75%. For the reverse and much more, see how to calculate percentages. Working with two quantities instead of one? The Ratio Calculator simplifies and solves proportions.

Frequently asked questions

How do I convert a fraction to a decimal?

Divide the numerator by the denominator. For 3/4, calculate 3 ÷ 4 = 0.75.

How can I tell if a fraction's decimal will repeat?

Reduce it to lowest terms and check the denominator. If its only prime factors are 2 and 5, the decimal terminates; otherwise it repeats.

How do I convert a fraction to a percentage?

Convert it to a decimal, then multiply by 100. 3/4 = 0.75 = 75%.

What is 1/3 as a decimal?

1/3 is 0.3333…, a repeating decimal — the 3 continues forever. It's often rounded to 0.33 or written with a bar over the 3.