This fraction to decimal calculator converts any fraction to its decimal expansion — and for recurring decimals, it finds and marks the repeating cycle exactly (like 1/7 = 0.(142857)).

Decimal (exact cycle shown) –
Type –
As a percent –
Rounded (4 dp) –

Some Decimals End. The Rest Repeat — and We Show Exactly Where

Part of our Math Calculators collection. For the reverse trip and mixed numbers, use the site's Fraction Calculator.

Worked Examples (Verified)

  • 7/12 (defaults) = 0.58(3) — two quiet digits, then 3 forever; as a percent 58.3333%
  • 1/7 = 0.(142857) — the famous six-digit cycle; every 1/7-family fraction (2/7, 3/7…) uses the same digits, rotated
  • 5/8 = 0.625 terminates: 8 = 2³, and denominators built only from 2s and 5s always terminate — the test is the prime factorization of the simplified denominator

The Terminating Test

  • Simplify the fraction first; then factor the denominator.
  • Only 2s and 5s (the factors of 10) → the decimal terminates.
  • Any other prime (3, 7, 11, 13…) → it repeats, with cycle length at most (denominator − 1) digits.
  • Mixed factors (12 = 2² × 3) → a non-repeating head (from the 2s/5s) then a repeating tail (from the 3): precisely the 0.58(3) pattern above.

Related Tools

Frequently Asked Questions

How do you convert a fraction to a decimal?

Divide the numerator by the denominator — long division generates the digits, and every fraction either terminates or falls into a repeating cycle (because remainders must eventually repeat). This calculator performs the division symbolically and marks the cycle in parentheses.

What is 7/12 as a decimal?

0.58333… exactly 0.58(3): the 3 repeats forever. Rounded to four places it's 0.5833, and as a percent 58.33%. The repeating tail exists because 12 = 2² × 3 contains a 3.

Which fractions terminate?

After simplifying, those whose denominators factor into only 2s and 5s: 1/8 (2³) → 0.125, 3/20 (2² × 5) → 0.15. Any other prime factor forces repetition — 1/6 (2 × 3) → 0.1(6), 1/7 (7) → 0.(142857).

What does 0.(142857) mean?

The parentheses (or an overbar) mark the repeating block: 0.(142857) = 0.142857142857… The block can be long — 1/97 cycles through 96 digits — this calculator detects cycles up to 200 digits by tracking remainders.

How do I turn the decimal back into a fraction?

Terminating: count places and write over 10ⁿ, then simplify (0.625 = 625/1000 = 5/8). Repeating: algebra — let x = 0.(142857), 10⁶x − x = 142857, so x = 142857/999999 = 1/7. The site's Fraction Calculator handles fraction arithmetic from there.

Is this fraction to decimal calculator free?

Yes — free, instant, no sign-up.