0.4555… as a Fraction

0.4555… (0.45 repeating) as a fraction is 41/90.

How to convert 0.4555… to a fraction

  1. Let x = 0.4555... (the underlined part, 5, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 45.555...
  3. Move the decimal point past the non-repeating digits too: 10x = 4.5555...
  4. Subtract to cancel the repeating tail: 100x − 10x = 45 − 4, so 90x = 41.
  5. Solve: x = 41/90. The greatest common divisor is 1, so x = 41/90 (already in lowest terms).

Check

Divide 41 by 90 on a calculator: 41 ÷ 90 = 0.4555555556… which matches 0.4555….

Similar repeating decimals

DecimalFraction
0.434343…43/99
0.444…4/9
0.454545…5/11
0.456456456…152/333
0.461461461…461/999
0.464646…46/99
0.4666…7/15
0.474747…47/99

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