0.027027027… as a Fraction

0.027027027… (0.027 repeating) as a fraction is 1/37.

How to convert 0.027027027… to a fraction

  1. Let x = 0.027027027... (the underlined part, 027, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 27.027027027...
  3. Subtract to cancel the repeating tail: 1000x − x = 27 − 0, so 999x = 27.
  4. Solve: x = 27/999. The greatest common divisor is 27, so x = 1/37.

Check

Divide 1 by 37 on a calculator: 1 ÷ 37 = 0.027027027… which matches 0.027027027….

Similar repeating decimals

DecimalFraction
0.012012012…4/333
0.012345012345012345…4115/333333
0.020202…2/99
0.0222…1/45
0.030303…1/33
0.0333…1/30
0.037037037…1/27
0.040404…4/99

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