0.363636… as a Fraction

0.363636… (0.36 repeating) as a fraction is 4/11.

How to convert 0.363636… to a fraction

  1. Let x = 0.363636... (the underlined part, 36, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 36.363636...
  3. Subtract to cancel the repeating tail: 100x − x = 36 − 0, so 99x = 36.
  4. Solve: x = 36/99. The greatest common divisor is 9, so x = 4/11.

Check

Divide 4 by 11 on a calculator: 4 ÷ 11 = 0.3636363636… which matches 0.363636….

Similar repeating decimals

DecimalFraction
0.3444…31/90
0.345345345…115/333
0.353535…35/99
0.3555…16/45
0.3666…11/30
0.373737…37/99
0.3777…17/45
0.383838…38/99

See also: 4/11 as a decimal.

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