0.012345012345012345… as a Fraction

0.012345012345012345… (0.012345 repeating) as a fraction is 4115/333333.

How to convert 0.012345012345012345… to a fraction

  1. Let x = 0.012345012345012345... (the underlined part, 012345, repeats forever).
  2. Move the decimal point past one full repeating block: 1000000x = 12345.012345012345012345...
  3. Subtract to cancel the repeating tail: 1000000x − x = 12345 − 0, so 999999x = 12345.
  4. Solve: x = 12345/999999. The greatest common divisor is 3, so x = 4115/333333.

Check

Divide 4115 by 333333 on a calculator: 4115 ÷ 333333 = 0.0123450123… which matches 0.012345012345012345….

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
0.012012012…4/333

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