9.777… as a Fraction

9.777… (9.7 repeating) as a fraction is 88/9. As a mixed number that is 9 7/9.

How to convert 9.777… to a fraction

  1. Let x = 9.777... (the underlined part, 7, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 97.777...
  3. Subtract to cancel the repeating tail: 10x − x = 97 − 9, so 9x = 88.
  4. Solve: x = 88/9. The greatest common divisor is 1, so x = 88/9 (already in lowest terms).

Since 88 is larger than 9, it can also be written as the mixed number 9 7/9.

Check

Divide 88 by 9 on a calculator: 88 ÷ 9 = 9.7777777778… which matches 9.777….

Similar repeating decimals

DecimalFraction
8.888…80/9
9.111…82/9
9.222…83/9
9.333…28/3
9.444…85/9
9.555…86/9
9.666…29/3
9.888…89/9

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