Decimal to fraction converter
Convert decimals, repeating decimals and fractions, or find the closest fraction with a small denominator.
A clear answer. Here’s how.
Terminating decimals become digits ÷ 10^k; a repeating decimal A.B(C) equals (ABC − AB) ÷ (10^k(10^m − 1)) for k fixed and m repeating digits. Fractions are reduced by the greatest common divisor with exact arbitrary-size integers. Long division finds the repeating block of any fraction. The closest-fraction mode uses continued fractions and semiconvergents to find the best fraction under a denominator limit. Scientific notation is not accepted.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- Value
- 0.1(6)
- Convert
- Decimal → fraction (brackets mark repeating digits)
- Largest denominator (closest-fraction mode)
- 1000
Example result
- Simplified fraction
- 1/6
- Mixed number
- 1/6
- Decimal
- 0.1(6)
- Percentage
- 16.6666666667%
- Terminating or repeating?
- Repeating, period 1
Fractions are exact (arbitrary-size integers) and reduced by the greatest common divisor. A fraction terminates only if its reduced denominator has no prime factors other than 2 and 5; digits in brackets repeat forever. Repeating blocks longer than 10,000 digits are cut off.