0.393939… as a Fraction

0.393939… (0.39 repeating) as a fraction is 13/33.

How to convert 0.393939… to a fraction

  1. Let x = 0.393939... (the underlined part, 39, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 39.393939...
  3. Subtract to cancel the repeating tail: 100x − x = 39 − 0, so 99x = 39.
  4. Solve: x = 39/99. The greatest common divisor is 3, so x = 13/33.

Check

Divide 13 by 33 on a calculator: 13 ÷ 33 = 0.3939393939… which matches 0.393939….

Similar repeating decimals

DecimalFraction
0.373737…37/99
0.3777…17/45
0.383838…38/99
0.384384384…128/333
0.3888…7/18
0.404040…40/99
0.4111…37/90
0.41333…31/75

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