0.9222… as a Fraction

0.9222… (0.92 repeating) as a fraction is 83/90.

How to convert 0.9222… to a fraction

  1. Let x = 0.9222... (the underlined part, 2, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 92.222...
  3. Move the decimal point past the non-repeating digits too: 10x = 9.2222...
  4. Subtract to cancel the repeating tail: 100x − 10x = 92 − 9, so 90x = 83.
  5. Solve: x = 83/90. The greatest common divisor is 1, so x = 83/90 (already in lowest terms).

Check

Divide 83 by 90 on a calculator: 83 ÷ 90 = 0.9222222222… which matches 0.9222….

Similar repeating decimals

DecimalFraction
0.909090…10/11
0.9111…41/45
0.91333…137/150
0.91666…11/12
0.919191…91/99
0.923923923…923/999
0.929292…92/99
0.9333…14/15

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