0.828282… as a Fraction

0.828282… (0.82 repeating) as a fraction is 82/99.

How to convert 0.828282… to a fraction

  1. Let x = 0.828282... (the underlined part, 82, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 82.828282...
  3. Subtract to cancel the repeating tail: 100x − x = 82 − 0, so 99x = 82.
  4. Solve: x = 82/99. The greatest common divisor is 1, so x = 82/99 (already in lowest terms).

Check

Divide 82 by 99 on a calculator: 82 ÷ 99 = 0.8282828283… which matches 0.828282….

Similar repeating decimals

DecimalFraction
0.8111…73/90
0.818181…9/11
0.8222…37/45
0.8333…5/6
0.83333…5/6
0.83666…251/300
0.838383…83/99
0.8444…38/45

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