8.222… as a Fraction

8.222… (8.2 repeating) as a fraction is 74/9. As a mixed number that is 8 2/9.

How to convert 8.222… to a fraction

  1. Let x = 8.222... (the underlined part, 2, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 82.222...
  3. Subtract to cancel the repeating tail: 10x − x = 82 − 8, so 9x = 74.
  4. Solve: x = 74/9. The greatest common divisor is 1, so x = 74/9 (already in lowest terms).

Since 74 is larger than 9, it can also be written as the mixed number 8 2/9.

Check

Divide 74 by 9 on a calculator: 74 ÷ 9 = 8.2222222222… which matches 8.222….

Similar repeating decimals

DecimalFraction
7.666…23/3
7.777…70/9
7.888…71/9
8.111…73/9
8.333…25/3
8.444…76/9
8.555…77/9
8.666…26/3

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