0.6777… as a Fraction

0.6777… (0.67 repeating) as a fraction is 61/90.

How to convert 0.6777… to a fraction

  1. Let x = 0.6777... (the underlined part, 7, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 67.777...
  3. Move the decimal point past the non-repeating digits too: 10x = 6.7777...
  4. Subtract to cancel the repeating tail: 100x − 10x = 67 − 6, so 90x = 61.
  5. Solve: x = 61/90. The greatest common divisor is 1, so x = 61/90 (already in lowest terms).

Check

Divide 61 by 90 on a calculator: 61 ÷ 90 = 0.6777777778… which matches 0.6777….

Similar repeating decimals

DecimalFraction
0.656565…65/99
0.666…2/3
0.676767…67/99
0.678678678…226/333
0.686868…68/99
0.6888…31/45
0.692692692…692/999
0.696969…23/33

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