7.222… as a Fraction

7.222… (7.2 repeating) as a fraction is 65/9. As a mixed number that is 7 2/9.

How to convert 7.222… to a fraction

  1. Let x = 7.222... (the underlined part, 2, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 72.222...
  3. Subtract to cancel the repeating tail: 10x − x = 72 − 7, so 9x = 65.
  4. Solve: x = 65/9. The greatest common divisor is 1, so x = 65/9 (already in lowest terms).

Since 65 is larger than 9, it can also be written as the mixed number 7 2/9.

Check

Divide 65 by 9 on a calculator: 65 ÷ 9 = 7.2222222222… which matches 7.222….

Similar repeating decimals

DecimalFraction
6.666…20/3
6.777…61/9
6.888…62/9
7.111…64/9
7.333…22/3
7.444…67/9
7.555…68/9
7.666…23/3

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