0.3666… as a Fraction

0.3666… (0.36 repeating) as a fraction is 11/30.

How to convert 0.3666… to a fraction

  1. Let x = 0.3666... (the underlined part, 6, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 36.666...
  3. Move the decimal point past the non-repeating digits too: 10x = 3.6666...
  4. Subtract to cancel the repeating tail: 100x − 10x = 36 − 3, so 90x = 33.
  5. Solve: x = 33/90. The greatest common divisor is 3, so x = 11/30.

Check

Divide 11 by 30 on a calculator: 11 ÷ 30 = 0.3666666667… which matches 0.3666….

Similar repeating decimals

DecimalFraction
0.345345345…115/333
0.353535…35/99
0.3555…16/45
0.363636…4/11
0.373737…37/99
0.3777…17/45
0.383838…38/99
0.384384384…128/333

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