CalcBrew

Decimal to Fraction Calculator

Turn any decimal into a fraction in lowest terms — with the work shown, just like you would write it out. Repeating decimals are handled too: type 0.33... or 0.1(6) and the calculator applies the nines method. A fraction-to-decimal converter with repeating-block detection is included below.

By Miikka · CalcBrew · Updated

Repeating decimals work too: type 0.33... (trailing dots) or 0.1(6) — digits in parentheses repeat.

Fraction

3/8

Improper fraction

3/8

The work

  1. 0.375 = 375/1,000 (3 decimal places → denominator 1,000)
  2. GCD(375, 1,000) = 125
  3. 375 ÷ 125 = 3 and 1,000 ÷ 125 = 8 → 3/8

Fraction to decimal

Exact decimal

0.41(6)

Rounded

0.416667

The digits in parentheses repeat forever: 0.41666…

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How the conversion works

A terminating decimal converts in two moves. Write the decimal digits over a power of ten, then simplify with the greatest common divisor: 0.75 = 75/100, and since GCD(75, 100) = 25, dividing both gives 3/4.

Repeating decimals need the nines method. For 0.1(6) — that is, 0.1666... — subtract the non-repeating digits from all the digits: 16 − 1 = 15. The denominator gets one 9 for each repeating digit and one 0 for each non-repeating digit: 90. So 0.1666... = 15/90 = 1/6 exactly. Whether a fraction terminates or repeats is decided entirely by its denominator: only prime factors 2 and 5 give a terminating decimal (the 2ᵃ·5ᵇ rule).

Common decimal–fraction conversions

DecimalFraction
0.11/10
0.1251/8
0.21/5
0.251/4
0.333...1/3
0.3753/8
0.42/5
0.51/2
0.63/5
0.6255/8
0.666...2/3
0.753/4
0.84/5
0.8757/8

Frequently asked questions

Cite this calculator
APACalcBrew. (2026). Decimal to Fraction Calculator. https://calcbrew.com/decimal-to-fraction
MLA“Decimal to Fraction Calculator.” CalcBrew, 2026, calcbrew.com/decimal-to-fraction.

Link to https://calcbrew.com/decimal-to-fraction. Results are estimates; cite the underlying formula or data source for academic work.

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