0.0333… as a Fraction

0.0333… (0.03 repeating) as a fraction is 1/30.

How to convert 0.0333… to a fraction

  1. Let x = 0.0333... (the underlined part, 3, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 3.333...
  3. Move the decimal point past the non-repeating digits too: 10x = 0.3333...
  4. Subtract to cancel the repeating tail: 100x − 10x = 3 − 0, so 90x = 3.
  5. Solve: x = 3/90. The greatest common divisor is 3, so x = 1/30.

Check

Divide 1 by 30 on a calculator: 1 ÷ 30 = 0.0333333333… which matches 0.0333….

Similar repeating decimals

DecimalFraction
0.020202…2/99
0.0222…1/45
0.027027027…1/37
0.030303…1/33
0.037037037…1/27
0.040404…4/99
0.0444…2/45
0.050505…5/99

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