0.2333… as a Fraction

0.2333… (0.23 repeating) as a fraction is 7/30.

How to convert 0.2333… to a fraction

  1. Let x = 0.2333... (the underlined part, 3, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 23.333...
  3. Move the decimal point past the non-repeating digits too: 10x = 2.3333...
  4. Subtract to cancel the repeating tail: 100x − 10x = 23 − 2, so 90x = 21.
  5. Solve: x = 21/90. The greatest common divisor is 3, so x = 7/30.

Check

Divide 7 by 30 on a calculator: 7 ÷ 30 = 0.2333333333… which matches 0.2333….

Similar repeating decimals

DecimalFraction
0.212121…7/33
0.222…2/9
0.230230230…230/999
0.232323…23/99
0.234234234…26/111
0.242424…8/33
0.2444…11/45
0.252525…25/99

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