0.838383… as a Fraction

0.838383… (0.83 repeating) as a fraction is 83/99.

How to convert 0.838383… to a fraction

  1. Let x = 0.838383... (the underlined part, 83, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 83.838383...
  3. Subtract to cancel the repeating tail: 100x − x = 83 − 0, so 99x = 83.
  4. Solve: x = 83/99. The greatest common divisor is 1, so x = 83/99 (already in lowest terms).

Check

Divide 83 by 99 on a calculator: 83 ÷ 99 = 0.8383838384… which matches 0.838383….

Similar repeating decimals

DecimalFraction
0.8222…37/45
0.828282…82/99
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0.83333…5/6
0.83666…251/300
0.8444…38/45
0.846846846…94/111
0.848484…28/33

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