0.012012012… as a Fraction

0.012012012… (0.012 repeating) as a fraction is 4/333.

How to convert 0.012012012… to a fraction

  1. Let x = 0.012012012... (the underlined part, 012, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 12.012012012...
  3. Subtract to cancel the repeating tail: 1000x − x = 12 − 0, so 999x = 12.
  4. Solve: x = 12/999. The greatest common divisor is 3, so x = 4/333.

Check

Divide 4 by 333 on a calculator: 4 ÷ 333 = 0.012012012… which matches 0.012012012….

Similar repeating decimals

DecimalFraction
0.005005005…5/999
0.006006006…2/333
0.007007007…7/999
0.008008008…8/999
0.009009009…1/111
0.010101…1/99
0.0111…1/90
0.012345012345012345…4115/333333

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