0.909090… as a Fraction

0.909090… (0.90 repeating) as a fraction is 10/11.

How to convert 0.909090… to a fraction

  1. Let x = 0.909090... (the underlined part, 90, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 90.909090...
  3. Subtract to cancel the repeating tail: 100x − x = 90 − 0, so 99x = 90.
  4. Solve: x = 90/99. The greatest common divisor is 9, so x = 10/11.

Check

Divide 10 by 11 on a calculator: 10 ÷ 11 = 0.9090909091… which matches 0.909090….

Similar repeating decimals

DecimalFraction
0.888…8/9
0.898989…89/99
0.9111…41/45
0.91333…137/150
0.91666…11/12
0.919191…91/99
0.9222…83/90
0.923923923…923/999

See also: 10/11 as a decimal.

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