6.777… as a Fraction

6.777… (6.7 repeating) as a fraction is 61/9. As a mixed number that is 6 7/9.

How to convert 6.777… to a fraction

  1. Let x = 6.777... (the underlined part, 7, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 67.777...
  3. Subtract to cancel the repeating tail: 10x − x = 67 − 6, so 9x = 61.
  4. Solve: x = 61/9. The greatest common divisor is 1, so x = 61/9 (already in lowest terms).

Since 61 is larger than 9, it can also be written as the mixed number 6 7/9.

Check

Divide 61 by 9 on a calculator: 61 ÷ 9 = 6.7777777778… which matches 6.777….

Similar repeating decimals

DecimalFraction
6.222…56/9
6.333…19/3
6.444…58/9
6.555…59/9
6.666…20/3
6.888…62/9
7.111…64/9
7.222…65/9

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