5.777… as a Fraction

5.777… (5.7 repeating) as a fraction is 52/9. As a mixed number that is 5 7/9.

How to convert 5.777… to a fraction

  1. Let x = 5.777... (the underlined part, 7, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 57.777...
  3. Subtract to cancel the repeating tail: 10x − x = 57 − 5, so 9x = 52.
  4. Solve: x = 52/9. The greatest common divisor is 1, so x = 52/9 (already in lowest terms).

Since 52 is larger than 9, it can also be written as the mixed number 5 7/9.

Check

Divide 52 by 9 on a calculator: 52 ÷ 9 = 5.7777777778… which matches 5.777….

Similar repeating decimals

DecimalFraction
5.222…47/9
5.333…16/3
5.444…49/9
5.555…50/9
5.666…17/3
5.888…53/9
6.111…55/9
6.222…56/9

See also: 52/9 as a mixed number.

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