0.91666… as a Fraction

0.91666… (0.916 repeating) as a fraction is 11/12.

How to convert 0.91666… to a fraction

  1. Let x = 0.91666... (the underlined part, 6, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 916.666...
  3. Move the decimal point past the non-repeating digits too: 100x = 91.6666...
  4. Subtract to cancel the repeating tail: 1000x − 100x = 916 − 91, so 900x = 825.
  5. Solve: x = 825/900. The greatest common divisor is 75, so x = 11/12.

Check

Divide 11 by 12 on a calculator: 11 ÷ 12 = 0.9166666667… which matches 0.91666….

Similar repeating decimals

DecimalFraction
0.909090…10/11
0.9111…41/45
0.91333…137/150
0.919191…91/99
0.9222…83/90
0.923923923…923/999
0.929292…92/99
0.9333…14/15

See also: 11/12 as a decimal.

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