0.8222… as a Fraction

0.8222… (0.82 repeating) as a fraction is 37/45.

How to convert 0.8222… to a fraction

  1. Let x = 0.8222... (the underlined part, 2, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 82.222...
  3. Move the decimal point past the non-repeating digits too: 10x = 8.2222...
  4. Subtract to cancel the repeating tail: 100x − 10x = 82 − 8, so 90x = 74.
  5. Solve: x = 74/90. The greatest common divisor is 2, so x = 37/45.

Check

Divide 37 by 45 on a calculator: 37 ÷ 45 = 0.8222222222… which matches 0.8222….

Similar repeating decimals

DecimalFraction
0.808080…80/99
0.8111…73/90
0.818181…9/11
0.828282…82/99
0.8333…5/6
0.83333…5/6
0.83666…251/300
0.838383…83/99

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