0.234234234… as a Fraction

0.234234234… (0.234 repeating) as a fraction is 26/111.

How to convert 0.234234234… to a fraction

  1. Let x = 0.234234234... (the underlined part, 234, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 234.234234234...
  3. Subtract to cancel the repeating tail: 1000x − x = 234 − 0, so 999x = 234.
  4. Solve: x = 234/999. The greatest common divisor is 9, so x = 26/111.

Check

Divide 26 by 111 on a calculator: 26 ÷ 111 = 0.2342342342… which matches 0.234234234….

Similar repeating decimals

DecimalFraction
0.222…2/9
0.230230230…230/999
0.232323…23/99
0.2333…7/30
0.242424…8/33
0.2444…11/45
0.252525…25/99
0.2555…23/90

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