0.6555… as a Fraction

0.6555… (0.65 repeating) as a fraction is 59/90.

How to convert 0.6555… to a fraction

  1. Let x = 0.6555... (the underlined part, 5, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 65.555...
  3. Move the decimal point past the non-repeating digits too: 10x = 6.5555...
  4. Subtract to cancel the repeating tail: 100x − 10x = 65 − 6, so 90x = 59.
  5. Solve: x = 59/90. The greatest common divisor is 1, so x = 59/90 (already in lowest terms).

Check

Divide 59 by 90 on a calculator: 59 ÷ 90 = 0.6555555556… which matches 0.6555….

Similar repeating decimals

DecimalFraction
0.6333…19/30
0.636363…7/11
0.6444…29/45
0.646464…64/99
0.656565…65/99
0.666…2/3
0.676767…67/99
0.6777…61/90

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