0.111… as a Fraction

0.111… (0.1 repeating) as a fraction is 1/9.

How to convert 0.111… to a fraction

  1. Let x = 0.111... (the underlined part, 1, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 1.111...
  3. Subtract to cancel the repeating tail: 10x − x = 1 − 0, so 9x = 1.
  4. Solve: x = 1/9. The greatest common divisor is 1, so x = 1/9 (already in lowest terms).

Check

Divide 1 by 9 on a calculator: 1 ÷ 9 = 0.1111111111… which matches 0.111….

Similar repeating decimals

DecimalFraction
0.0888…4/45
0.090909…1/11
0.101010…10/99
0.121212…4/33
0.1222…11/90
0.123123123…41/333
0.131313…13/99
0.1333…2/15

See also: 1/9 as a decimal.

Another decimal? Browse the repeating decimal to fraction chart, the terminating decimal chart, or use the decimal to fraction converter.