2.222… as a Fraction

2.222… (2.2 repeating) as a fraction is 20/9. As a mixed number that is 2 2/9.

How to convert 2.222… to a fraction

  1. Let x = 2.222... (the underlined part, 2, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 22.222...
  3. Subtract to cancel the repeating tail: 10x − x = 22 − 2, so 9x = 20.
  4. Solve: x = 20/9. The greatest common divisor is 1, so x = 20/9 (already in lowest terms).

Since 20 is larger than 9, it can also be written as the mixed number 2 2/9.

Check

Divide 20 by 9 on a calculator: 20 ÷ 9 = 2.2222222222… which matches 2.222….

Similar repeating decimals

DecimalFraction
1.8333…11/6
1.888…17/9
2.111…19/9
2.1666…13/6
2.333…7/3
2.444…22/9
2.5333…38/15
2.555…23/9

See also: 20/9 as a mixed number.

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