0.777… as a Fraction

0.777… (0.7 repeating) as a fraction is 7/9.

How to convert 0.777… to a fraction

1. Let x = 0.777... (the underlined part, 7, repeats forever).
2. Move the decimal point past one full repeating block: 10x = 7.777...
3. Subtract to cancel the repeating tail: 10x − x = 7 − 0, so 9x = 7.
4. Solve: x = 7/9. The greatest common divisor is 1, so x = 7/9 (already in lowest terms).

Check

Divide 7 by 9 on a calculator: 7 ÷ 9 = 0.7777777778… which matches 0.777….

Similar repeating decimals

See also: 7/9 as a decimal.

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