8.777… as a Fraction

8.777… (8.7 repeating) as a fraction is 79/9. As a mixed number that is 8 7/9.

How to convert 8.777… to a fraction

  1. Let x = 8.777... (the underlined part, 7, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 87.777...
  3. Subtract to cancel the repeating tail: 10x − x = 87 − 8, so 9x = 79.
  4. Solve: x = 79/9. The greatest common divisor is 1, so x = 79/9 (already in lowest terms).

Since 79 is larger than 9, it can also be written as the mixed number 8 7/9.

Check

Divide 79 by 9 on a calculator: 79 ÷ 9 = 8.7777777778… which matches 8.777….

Similar repeating decimals

DecimalFraction
8.333…25/3
8.444…76/9
8.555…77/9
8.666…26/3
8.888…80/9
9.111…82/9
9.222…83/9
9.333…28/3

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