0.007007007… as a Fraction

0.007007007… (0.007 repeating) as a fraction is 7/999.

How to convert 0.007007007… to a fraction

  1. Let x = 0.007007007... (the underlined part, 007, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 7.007007007...
  3. Subtract to cancel the repeating tail: 1000x − x = 7 − 0, so 999x = 7.
  4. Solve: x = 7/999. The greatest common divisor is 1, so x = 7/999 (already in lowest terms).

Check

Divide 7 by 999 on a calculator: 7 ÷ 999 = 0.007007007… which matches 0.007007007….

Similar repeating decimals

DecimalFraction
0.003003003…1/333
0.004004004…4/999
0.005005005…5/999
0.006006006…2/333
0.008008008…8/999
0.009009009…1/111
0.010101…1/99
0.0111…1/90

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