Formula
decimal = numerator ÷ denominator
- Repeating digits are shown in brackets: 1/3 = 0.(3), 1/6 = 0.1(6).
A fraction is a division. The decimal either stops or repeats forever.
Worked examples
22/7
- Numerator
- 22
- Denominator
- 7
Decimal
3.1428571429
Exact decimal expansion: 3.(142857)
Simplified fraction: 22/7
Percentage: 314.285714%
3/8
- Numerator
- 3
- Denominator
- 8
Decimal
0.375
Exact decimal expansion: 0.375
Simplified fraction: 3/8
Percentage: 37.5%
How it works
Long division gives the digits one at a time. Each step leaves a remainder; as soon as a remainder repeats, the digits repeat from there. 1 ÷ 7 produces the cycle 142857 and so 1/7 = 0.(142857).
A fraction in lowest terms terminates only if its denominator has no prime factors other than 2 and 5 — so 3/8 = 0.375 stops, but 1/3 and 1/7 never do. The tool reduces the fraction first, so 2/6 reports 0.(3) like 1/3.
To go the other way, use Decimal to Fraction Calculator. For a percentage use Fraction to Percentage Calculator.
Assumptions and limits
- Whole-number numerator and denominator only.
- Repeating cycles longer than 60 digits are cut off and flagged.