0.4777… as a Fraction

0.4777… (0.47 repeating) as a fraction is 43/90.

How to convert 0.4777… to a fraction

  1. Let x = 0.4777... (the underlined part, 7, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 47.777...
  3. Move the decimal point past the non-repeating digits too: 10x = 4.7777...
  4. Subtract to cancel the repeating tail: 100x − 10x = 47 − 4, so 90x = 43.
  5. Solve: x = 43/90. The greatest common divisor is 1, so x = 43/90 (already in lowest terms).

Check

Divide 43 by 90 on a calculator: 43 ÷ 90 = 0.4777777778… which matches 0.4777….

Similar repeating decimals

DecimalFraction
0.456456456…152/333
0.461461461…461/999
0.464646…46/99
0.4666…7/15
0.474747…47/99
0.484848…16/33
0.4888…22/45
0.494949…49/99

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