0.009009009… as a Fraction

0.009009009… (0.009 repeating) as a fraction is 1/111.

How to convert 0.009009009… to a fraction

  1. Let x = 0.009009009... (the underlined part, 009, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 9.009009009...
  3. Subtract to cancel the repeating tail: 1000x − x = 9 − 0, so 999x = 9.
  4. Solve: x = 9/999. The greatest common divisor is 9, so x = 1/111.

Check

Divide 1 by 111 on a calculator: 1 ÷ 111 = 0.009009009… which matches 0.009009009….

Similar repeating decimals

DecimalFraction
0.005005005…5/999
0.006006006…2/333
0.007007007…7/999
0.008008008…8/999
0.010101…1/99
0.0111…1/90
0.012012012…4/333
0.012345012345012345…4115/333333

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