0.383838… as a Fraction

0.383838… (0.38 repeating) as a fraction is 38/99.

How to convert 0.383838… to a fraction

  1. Let x = 0.383838... (the underlined part, 38, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 38.383838...
  3. Subtract to cancel the repeating tail: 100x − x = 38 − 0, so 99x = 38.
  4. Solve: x = 38/99. The greatest common divisor is 1, so x = 38/99 (already in lowest terms).

Check

Divide 38 by 99 on a calculator: 38 ÷ 99 = 0.3838383838… which matches 0.383838….

Similar repeating decimals

DecimalFraction
0.363636…4/11
0.3666…11/30
0.373737…37/99
0.3777…17/45
0.384384384…128/333
0.3888…7/18
0.393939…13/33
0.404040…40/99

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