0.545454… as a Fraction

0.545454… (0.54 repeating) as a fraction is 6/11.

How to convert 0.545454… to a fraction

  1. Let x = 0.545454... (the underlined part, 54, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 54.545454...
  3. Subtract to cancel the repeating tail: 100x − x = 54 − 0, so 99x = 54.
  4. Solve: x = 54/99. The greatest common divisor is 9, so x = 6/11.

Check

Divide 6 by 11 on a calculator: 6 ÷ 11 = 0.5454545455… which matches 0.545454….

Similar repeating decimals

DecimalFraction
0.525252…52/99
0.5333…8/15
0.535353…53/99
0.538538538…538/999
0.5444…49/90
0.555…5/9
0.565656…56/99
0.5666…17/30

See also: 6/11 as a decimal.

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