0.081081081… as a Fraction

0.081081081… (0.081 repeating) as a fraction is 3/37.

How to convert 0.081081081… to a fraction

  1. Let x = 0.081081081... (the underlined part, 081, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 81.081081081...
  3. Subtract to cancel the repeating tail: 1000x − x = 81 − 0, so 999x = 81.
  4. Solve: x = 81/999. The greatest common divisor is 27, so x = 3/37.

Check

Divide 3 by 37 on a calculator: 3 ÷ 37 = 0.0810810811… which matches 0.081081081….

Similar repeating decimals

DecimalFraction
0.074074074…2/27
0.076076076…76/999
0.076923076923076923…1/13
0.0777…7/90
0.080808…8/99
0.08333…1/12
0.08666…13/150
0.0888…4/45

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