0.474747… as a Fraction

0.474747… (0.47 repeating) as a fraction is 47/99.

How to convert 0.474747… to a fraction

  1. Let x = 0.474747... (the underlined part, 47, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 47.474747...
  3. Subtract to cancel the repeating tail: 100x − x = 47 − 0, so 99x = 47.
  4. Solve: x = 47/99. The greatest common divisor is 1, so x = 47/99 (already in lowest terms).

Check

Divide 47 by 99 on a calculator: 47 ÷ 99 = 0.4747474747… which matches 0.474747….

Similar repeating decimals

DecimalFraction
0.4555…41/90
0.456456456…152/333
0.461461461…461/999
0.464646…46/99
0.4666…7/15
0.4777…43/90
0.484848…16/33
0.4888…22/45

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