0.090909… as a Fraction

0.090909… (0.09 repeating) as a fraction is 1/11.

How to convert 0.090909… to a fraction

  1. Let x = 0.090909... (the underlined part, 09, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 9.090909...
  3. Subtract to cancel the repeating tail: 100x − x = 9 − 0, so 99x = 9.
  4. Solve: x = 9/99. The greatest common divisor is 9, so x = 1/11.

Check

Divide 1 by 11 on a calculator: 1 ÷ 11 = 0.0909090909… which matches 0.090909….

Similar repeating decimals

DecimalFraction
0.076923076923076923…1/13
0.0777…7/90
0.080808…8/99
0.081081081…3/37
0.08333…1/12
0.08666…13/150
0.0888…4/45
0.101010…10/99

See also: 1/11 as a decimal.

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