0.678678678… as a Fraction

0.678678678… (0.678 repeating) as a fraction is 226/333.

How to convert 0.678678678… to a fraction

  1. Let x = 0.678678678... (the underlined part, 678, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 678.678678678...
  3. Subtract to cancel the repeating tail: 1000x − x = 678 − 0, so 999x = 678.
  4. Solve: x = 678/999. The greatest common divisor is 3, so x = 226/333.

Check

Divide 226 by 333 on a calculator: 226 ÷ 333 = 0.6786786787… which matches 0.678678678….

Similar repeating decimals

DecimalFraction
0.656565…65/99
0.666…2/3
0.676767…67/99
0.6777…61/90
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.