0.003003003… as a Fraction

0.003003003… (0.003 repeating) as a fraction is 1/333.

How to convert 0.003003003… to a fraction

  1. Let x = 0.003003003... (the underlined part, 003, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 3.003003003...
  3. Subtract to cancel the repeating tail: 1000x − x = 3 − 0, so 999x = 3.
  4. Solve: x = 3/999. The greatest common divisor is 3, so x = 1/333.

Check

Divide 1 by 333 on a calculator: 1 ÷ 333 = 0.003003003… which matches 0.003003003….

Similar repeating decimals

DecimalFraction
0.001001001…1/999
0.002002002…2/999
0.004004004…4/999
0.005005005…5/999
0.006006006…2/333
0.007007007…7/999
0.008008008…8/999
0.009009009…1/111

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