0.0555… as a Fraction

0.0555… (0.05 repeating) as a fraction is 1/18.

How to convert 0.0555… to a fraction

  1. Let x = 0.0555... (the underlined part, 5, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 5.555...
  3. Move the decimal point past the non-repeating digits too: 10x = 0.5555...
  4. Subtract to cancel the repeating tail: 100x − 10x = 5 − 0, so 90x = 5.
  5. Solve: x = 5/90. The greatest common divisor is 5, so x = 1/18.

Check

Divide 1 by 18 on a calculator: 1 ÷ 18 = 0.0555555556… which matches 0.0555….

Similar repeating decimals

DecimalFraction
0.037037037…1/27
0.040404…4/99
0.0444…2/45
0.050505…5/99
0.054054054…2/37
0.060606…2/33
0.0666…1/15
0.070707…7/99

See also: 1/18 as a decimal.

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