0.222… as a Fraction

0.222… (0.2 repeating) as a fraction is 2/9.

How to convert 0.222… to a fraction

  1. Let x = 0.222... (the underlined part, 2, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 2.222...
  3. Subtract to cancel the repeating tail: 10x − x = 2 − 0, so 9x = 2.
  4. Solve: x = 2/9. The greatest common divisor is 1, so x = 2/9 (already in lowest terms).

Check

Divide 2 by 9 on a calculator: 2 ÷ 9 = 0.2222222222… which matches 0.222….

Similar repeating decimals

DecimalFraction
0.202020…20/99
0.2111…19/90
0.212121…7/33
0.230230230…230/999
0.232323…23/99
0.2333…7/30
0.234234234…26/111
0.242424…8/33

See also: 2/9 as a decimal.

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