0.454545… as a Fraction

0.454545… (0.45 repeating) as a fraction is 5/11.

How to convert 0.454545… to a fraction

  1. Let x = 0.454545... (the underlined part, 45, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 45.454545...
  3. Subtract to cancel the repeating tail: 100x − x = 45 − 0, so 99x = 45.
  4. Solve: x = 45/99. The greatest common divisor is 9, so x = 5/11.

Check

Divide 5 by 11 on a calculator: 5 ÷ 11 = 0.4545454545… which matches 0.454545….

Similar repeating decimals

DecimalFraction
0.434343…43/99
0.444…4/9
0.4555…41/90
0.456456456…152/333
0.461461461…461/999
0.464646…46/99
0.4666…7/15
0.474747…47/99

See also: 5/11 as a decimal.

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