0.008008008… as a Fraction

0.008008008… (0.008 repeating) as a fraction is 8/999.

How to convert 0.008008008… to a fraction

  1. Let x = 0.008008008... (the underlined part, 008, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 8.008008008...
  3. Subtract to cancel the repeating tail: 1000x − x = 8 − 0, so 999x = 8.
  4. Solve: x = 8/999. The greatest common divisor is 1, so x = 8/999 (already in lowest terms).

Check

Divide 8 by 999 on a calculator: 8 ÷ 999 = 0.008008008… which matches 0.008008008….

Similar repeating decimals

DecimalFraction
0.004004004…4/999
0.005005005…5/999
0.006006006…2/333
0.007007007…7/999
0.009009009…1/111
0.010101…1/99
0.0111…1/90
0.012012012…4/333

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