0.9111… as a Fraction

0.9111… (0.91 repeating) as a fraction is 41/45.

How to convert 0.9111… to a fraction

  1. Let x = 0.9111... (the underlined part, 1, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 91.111...
  3. Move the decimal point past the non-repeating digits too: 10x = 9.1111...
  4. Subtract to cancel the repeating tail: 100x − 10x = 91 − 9, so 90x = 82.
  5. Solve: x = 82/90. The greatest common divisor is 2, so x = 41/45.

Check

Divide 41 by 45 on a calculator: 41 ÷ 45 = 0.9111111111… which matches 0.9111….

Similar repeating decimals

DecimalFraction
0.898989…89/99
0.909090…10/11
0.91333…137/150
0.91666…11/12
0.919191…91/99
0.9222…83/90
0.923923923…923/999
0.929292…92/99

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