0.8111… as a Fraction

0.8111… (0.81 repeating) as a fraction is 73/90.

How to convert 0.8111… to a fraction

  1. Let x = 0.8111... (the underlined part, 1, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 81.111...
  3. Move the decimal point past the non-repeating digits too: 10x = 8.1111...
  4. Subtract to cancel the repeating tail: 100x − 10x = 81 − 8, so 90x = 73.
  5. Solve: x = 73/90. The greatest common divisor is 1, so x = 73/90 (already in lowest terms).

Check

Divide 73 by 90 on a calculator: 73 ÷ 90 = 0.8111111111… which matches 0.8111….

Similar repeating decimals

DecimalFraction
0.7888…71/90
0.789789789…263/333
0.797979…79/99
0.808080…80/99
0.818181…9/11
0.8222…37/45
0.828282…82/99
0.8333…5/6

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