0.83333… as a Fraction

0.83333… (0.833 repeating) as a fraction is 5/6.

How to convert 0.83333… to a fraction

  1. Let x = 0.83333... (the underlined part, 3, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 833.333...
  3. Move the decimal point past the non-repeating digits too: 100x = 83.3333...
  4. Subtract to cancel the repeating tail: 1000x − 100x = 833 − 83, so 900x = 750.
  5. Solve: x = 750/900. The greatest common divisor is 150, so x = 5/6.

Check

Divide 5 by 6 on a calculator: 5 ÷ 6 = 0.8333333333… which matches 0.83333….

Similar repeating decimals

DecimalFraction
0.818181…9/11
0.8222…37/45
0.828282…82/99
0.8333…5/6
0.83666…251/300
0.838383…83/99
0.8444…38/45
0.846846846…94/111

See also: 5/6 as a decimal.

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