0.464646… as a Fraction

0.464646… (0.46 repeating) as a fraction is 46/99.

How to convert 0.464646… to a fraction

  1. Let x = 0.464646... (the underlined part, 46, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 46.464646...
  3. Subtract to cancel the repeating tail: 100x − x = 46 − 0, so 99x = 46.
  4. Solve: x = 46/99. The greatest common divisor is 1, so x = 46/99 (already in lowest terms).

Check

Divide 46 by 99 on a calculator: 46 ÷ 99 = 0.4646464646… which matches 0.464646….

Similar repeating decimals

DecimalFraction
0.444…4/9
0.454545…5/11
0.4555…41/90
0.456456456…152/333
0.461461461…461/999
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.