0.006006006… as a Fraction

0.006006006… (0.006 repeating) as a fraction is 2/333.

How to convert 0.006006006… to a fraction

  1. Let x = 0.006006006... (the underlined part, 006, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 6.006006006...
  3. Subtract to cancel the repeating tail: 1000x − x = 6 − 0, so 999x = 6.
  4. Solve: x = 6/999. The greatest common divisor is 3, so x = 2/333.

Check

Divide 2 by 333 on a calculator: 2 ÷ 333 = 0.006006006… which matches 0.006006006….

Similar repeating decimals

DecimalFraction
0.002002002…2/999
0.003003003…1/333
0.004004004…4/999
0.005005005…5/999
0.007007007…7/999
0.008008008…8/999
0.009009009…1/111
0.010101…1/99

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