0.676767… as a Fraction

0.676767… (0.67 repeating) as a fraction is 67/99.

How to convert 0.676767… to a fraction

  1. Let x = 0.676767... (the underlined part, 67, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 67.676767...
  3. Subtract to cancel the repeating tail: 100x − x = 67 − 0, so 99x = 67.
  4. Solve: x = 67/99. The greatest common divisor is 1, so x = 67/99 (already in lowest terms).

Check

Divide 67 by 99 on a calculator: 67 ÷ 99 = 0.6767676768… which matches 0.676767….

Similar repeating decimals

DecimalFraction
0.656565…65/99
0.666…2/3
0.6777…61/90
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.