4.777… as a Fraction

4.777… (4.7 repeating) as a fraction is 43/9. As a mixed number that is 4 7/9.

How to convert 4.777… to a fraction

  1. Let x = 4.777... (the underlined part, 7, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 47.777...
  3. Subtract to cancel the repeating tail: 10x − x = 47 − 4, so 9x = 43.
  4. Solve: x = 43/9. The greatest common divisor is 1, so x = 43/9 (already in lowest terms).

Since 43 is larger than 9, it can also be written as the mixed number 4 7/9.

Check

Divide 43 by 9 on a calculator: 43 ÷ 9 = 4.7777777778… which matches 4.777….

Similar repeating decimals

DecimalFraction
4.222…38/9
4.333…13/3
4.444…40/9
4.555…41/9
4.666…14/3
4.888…44/9
5.111…46/9
5.222…47/9

See also: 43/9 as a mixed number.

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