0.656565… as a Fraction

0.656565… (0.65 repeating) as a fraction is 65/99.

How to convert 0.656565… to a fraction

  1. Let x = 0.656565... (the underlined part, 65, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 65.656565...
  3. Subtract to cancel the repeating tail: 100x − x = 65 − 0, so 99x = 65.
  4. Solve: x = 65/99. The greatest common divisor is 1, so x = 65/99 (already in lowest terms).

Check

Divide 65 by 99 on a calculator: 65 ÷ 99 = 0.6565656566… which matches 0.656565….

Similar repeating decimals

DecimalFraction
0.636363…7/11
0.6444…29/45
0.646464…64/99
0.6555…59/90
0.666…2/3
0.676767…67/99
0.6777…61/90
0.678678678…226/333

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