7.777… as a Fraction

7.777… (7.7 repeating) as a fraction is 70/9. As a mixed number that is 7 7/9.

How to convert 7.777… to a fraction

  1. Let x = 7.777... (the underlined part, 7, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 77.777...
  3. Subtract to cancel the repeating tail: 10x − x = 77 − 7, so 9x = 70.
  4. Solve: x = 70/9. The greatest common divisor is 1, so x = 70/9 (already in lowest terms).

Since 70 is larger than 9, it can also be written as the mixed number 7 7/9.

Check

Divide 70 by 9 on a calculator: 70 ÷ 9 = 7.7777777778… which matches 7.777….

Similar repeating decimals

DecimalFraction
7.222…65/9
7.333…22/3
7.444…67/9
7.555…68/9
7.666…23/3
7.888…71/9
8.111…73/9
8.222…74/9

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