3.222… as a Fraction

3.222… (3.2 repeating) as a fraction is 29/9. As a mixed number that is 3 2/9.

How to convert 3.222… to a fraction

  1. Let x = 3.222... (the underlined part, 2, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 32.222...
  3. Subtract to cancel the repeating tail: 10x − x = 32 − 3, so 9x = 29.
  4. Solve: x = 29/9. The greatest common divisor is 1, so x = 29/9 (already in lowest terms).

Since 29 is larger than 9, it can also be written as the mixed number 3 2/9.

Check

Divide 29 by 9 on a calculator: 29 ÷ 9 = 3.2222222222… which matches 3.222….

Similar repeating decimals

DecimalFraction
2.777…25/9
2.888…26/9
3.111…28/9
3.333…10/3
3.444…31/9
3.555…32/9
3.666…11/3
3.777…34/9

See also: 29/9 as a mixed number.

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