0.123123123… as a Fraction

0.123123123… (0.123 repeating) as a fraction is 41/333.

How to convert 0.123123123… to a fraction

  1. Let x = 0.123123123... (the underlined part, 123, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 123.123123123...
  3. Subtract to cancel the repeating tail: 1000x − x = 123 − 0, so 999x = 123.
  4. Solve: x = 123/999. The greatest common divisor is 3, so x = 41/333.

Check

Divide 41 by 333 on a calculator: 41 ÷ 333 = 0.1231231231… which matches 0.123123123….

Similar repeating decimals

DecimalFraction
0.111…1/9
0.121212…4/33
0.1222…11/90
0.131313…13/99
0.1333…2/15
0.135135135…5/37
0.141414…14/99
0.142142142…142/999

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