0.030303… as a Fraction

0.030303… (0.03 repeating) as a fraction is 1/33.

How to convert 0.030303… to a fraction

  1. Let x = 0.030303... (the underlined part, 03, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 3.030303...
  3. Subtract to cancel the repeating tail: 100x − x = 3 − 0, so 99x = 3.
  4. Solve: x = 3/99. The greatest common divisor is 3, so x = 1/33.

Check

Divide 1 by 33 on a calculator: 1 ÷ 33 = 0.0303030303… which matches 0.030303….

Similar repeating decimals

DecimalFraction
0.012345012345012345…4115/333333
0.020202…2/99
0.0222…1/45
0.027027027…1/37
0.0333…1/30
0.037037037…1/27
0.040404…4/99
0.0444…2/45

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