0.456456456… as a Fraction

0.456456456… (0.456 repeating) as a fraction is 152/333.

How to convert 0.456456456… to a fraction

  1. Let x = 0.456456456... (the underlined part, 456, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 456.456456456...
  3. Subtract to cancel the repeating tail: 1000x − x = 456 − 0, so 999x = 456.
  4. Solve: x = 456/999. The greatest common divisor is 3, so x = 152/333.

Check

Divide 152 by 333 on a calculator: 152 ÷ 333 = 0.4564564565… which matches 0.456456456….

Similar repeating decimals

DecimalFraction
0.444…4/9
0.454545…5/11
0.4555…41/90
0.461461461…461/999
0.464646…46/99
0.4666…7/15
0.474747…47/99
0.4777…43/90

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