0.6888… as a Fraction

0.6888… (0.68 repeating) as a fraction is 31/45.

How to convert 0.6888… to a fraction

  1. Let x = 0.6888... (the underlined part, 8, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 68.888...
  3. Move the decimal point past the non-repeating digits too: 10x = 6.8888...
  4. Subtract to cancel the repeating tail: 100x − 10x = 68 − 6, so 90x = 62.
  5. Solve: x = 62/90. The greatest common divisor is 2, so x = 31/45.

Check

Divide 31 by 45 on a calculator: 31 ÷ 45 = 0.6888888889… which matches 0.6888….

Similar repeating decimals

DecimalFraction
0.666…2/3
0.676767…67/99
0.6777…61/90
0.678678678…226/333
0.686868…68/99
0.692692692…692/999
0.696969…23/33
0.707070…70/99

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