FractionReference

Repeating decimal to fraction

Write the repeating block in parentheses — 0.(3) for 0.333…, 0.1(6) for 0.1666… — and get the exact fraction. This page never guesses whether a long decimal was meant to repeat; the notation says so.

Try:

Worked examples

Repeating decimalExact fraction
0.(3) 1/3
0.(6) 2/3
0.1(6) 1/6
0.(142857) 1/7
0.8(3) 5/6
0.(09) 1/11

Common questions

How do I write a repeating decimal here?
Put the repeating block in parentheses: 0.(3) means 0.333… forever, and 0.1(6) means 0.1666… — a fixed 1, then a repeating 6. The parentheses stand in for the overline used in print.
Why not just type lots of digits?
Because 0.333333 is exactly 333333/1000000, not 1/3, and this site will not guess that you meant the digits to continue. The parentheses say it explicitly, so the conversion can be exact.
What fraction is 0.999… repeating?
0.(9) equals exactly 1. The construction 9/9 = 1 is not a trick; the two notations name the same number.
Where this comes from. Exact rational arithmetic on the values shown — fractions are pairs of integers until display, and inch–metric conversion uses 25.4 mm to the inch, exact by definition since 1959. See the full methodology.