0.002002002… as a Fraction

0.002002002… (0.002 repeating) as a fraction is 2/999.

How to convert 0.002002002… to a fraction

  1. Let x = 0.002002002... (the underlined part, 002, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 2.002002002...
  3. Subtract to cancel the repeating tail: 1000x − x = 2 − 0, so 999x = 2.
  4. Solve: x = 2/999. The greatest common divisor is 1, so x = 2/999 (already in lowest terms).

Check

Divide 2 by 999 on a calculator: 2 ÷ 999 = 0.002002002… which matches 0.002002002….

Similar repeating decimals

DecimalFraction
0.001001001…1/999
0.003003003…1/333
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.