0.818181… as a Fraction

0.818181… (0.81 repeating) as a fraction is 9/11.

How to convert 0.818181… to a fraction

  1. Let x = 0.818181... (the underlined part, 81, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 81.818181...
  3. Subtract to cancel the repeating tail: 100x − x = 81 − 0, so 99x = 81.
  4. Solve: x = 81/99. The greatest common divisor is 9, so x = 9/11.

Check

Divide 9 by 11 on a calculator: 9 ÷ 11 = 0.8181818182… which matches 0.818181….

Similar repeating decimals

DecimalFraction
0.808080…80/99
0.8111…73/90
0.8222…37/45
0.828282…82/99
0.8333…5/6
0.83333…5/6
0.83666…251/300
0.838383…83/99

See also: 9/11 as a decimal.

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