0.001001001… as a Fraction

0.001001001… (0.001 repeating) as a fraction is 1/999.

How to convert 0.001001001… to a fraction

  1. Let x = 0.001001001... (the underlined part, 001, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 1.001001001...
  3. Subtract to cancel the repeating tail: 1000x − x = 1 − 0, so 999x = 1.
  4. Solve: x = 1/999. The greatest common divisor is 1, so x = 1/999 (already in lowest terms).

Check

Divide 1 by 999 on a calculator: 1 ÷ 999 = 0.001001001… which matches 0.001001001….

Similar repeating decimals

DecimalFraction
0.002002002…2/999
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.