0.054054054… as a Fraction

0.054054054… (0.054 repeating) as a fraction is 2/37.

How to convert 0.054054054… to a fraction

  1. Let x = 0.054054054... (the underlined part, 054, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 54.054054054...
  3. Subtract to cancel the repeating tail: 1000x − x = 54 − 0, so 999x = 54.
  4. Solve: x = 54/999. The greatest common divisor is 27, so x = 2/37.

Check

Divide 2 by 37 on a calculator: 2 ÷ 37 = 0.0540540541… which matches 0.054054054….

Similar repeating decimals

DecimalFraction
0.037037037…1/27
0.040404…4/99
0.0444…2/45
0.050505…5/99
0.0555…1/18
0.060606…2/33
0.0666…1/15
0.070707…7/99

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