6.222… as a Fraction

6.222… (6.2 repeating) as a fraction is 56/9. As a mixed number that is 6 2/9.

How to convert 6.222… to a fraction

  1. Let x = 6.222... (the underlined part, 2, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 62.222...
  3. Subtract to cancel the repeating tail: 10x − x = 62 − 6, so 9x = 56.
  4. Solve: x = 56/9. The greatest common divisor is 1, so x = 56/9 (already in lowest terms).

Since 56 is larger than 9, it can also be written as the mixed number 6 2/9.

Check

Divide 56 by 9 on a calculator: 56 ÷ 9 = 6.2222222222… which matches 6.222….

Similar repeating decimals

DecimalFraction
5.666…17/3
5.777…52/9
5.888…53/9
6.111…55/9
6.333…19/3
6.444…58/9
6.555…59/9
6.666…20/3

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