0.636363… as a Fraction

0.636363… (0.63 repeating) as a fraction is 7/11.

How to convert 0.636363… to a fraction

  1. Let x = 0.636363... (the underlined part, 63, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 63.636363...
  3. Subtract to cancel the repeating tail: 100x − x = 63 − 0, so 99x = 63.
  4. Solve: x = 63/99. The greatest common divisor is 9, so x = 7/11.

Check

Divide 7 by 11 on a calculator: 7 ÷ 11 = 0.6363636364… which matches 0.636363….

Similar repeating decimals

DecimalFraction
0.616161…61/99
0.6222…28/45
0.626262…62/99
0.6333…19/30
0.6444…29/45
0.646464…64/99
0.6555…59/90
0.656565…65/99

See also: 7/11 as a decimal.

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