9.222… as a Fraction

9.222… (9.2 repeating) as a fraction is 83/9. As a mixed number that is 9 2/9.

How to convert 9.222… to a fraction

  1. Let x = 9.222... (the underlined part, 2, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 92.222...
  3. Subtract to cancel the repeating tail: 10x − x = 92 − 9, so 9x = 83.
  4. Solve: x = 83/9. The greatest common divisor is 1, so x = 83/9 (already in lowest terms).

Since 83 is larger than 9, it can also be written as the mixed number 9 2/9.

Check

Divide 83 by 9 on a calculator: 83 ÷ 9 = 9.2222222222… which matches 9.222….

Similar repeating decimals

DecimalFraction
8.666…26/3
8.777…79/9
8.888…80/9
9.111…82/9
9.333…28/3
9.444…85/9
9.555…86/9
9.666…29/3

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