0.0111… as a Fraction

0.0111… (0.01 repeating) as a fraction is 1/90.

How to convert 0.0111… to a fraction

  1. Let x = 0.0111... (the underlined part, 1, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 1.111...
  3. Move the decimal point past the non-repeating digits too: 10x = 0.1111...
  4. Subtract to cancel the repeating tail: 100x − 10x = 1 − 0, so 90x = 1.
  5. Solve: x = 1/90. The greatest common divisor is 1, so x = 1/90 (already in lowest terms).

Check

Divide 1 by 90 on a calculator: 1 ÷ 90 = 0.0111111111… which matches 0.0111….

Similar repeating decimals

DecimalFraction
0.005005005…5/999
0.006006006…2/333
0.007007007…7/999
0.008008008…8/999
0.009009009…1/111
0.010101…1/99
0.012012012…4/333
0.012345012345012345…4115/333333

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