2.333… as a Fraction

2.333… (2.3 repeating) as a fraction is 7/3. As a mixed number that is 2 1/3.

How to convert 2.333… to a fraction

  1. Let x = 2.333... (the underlined part, 3, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 23.333...
  3. Subtract to cancel the repeating tail: 10x − x = 23 − 2, so 9x = 21.
  4. Solve: x = 21/9. The greatest common divisor is 3, so x = 7/3.

Since 7 is larger than 3, it can also be written as the mixed number 2 1/3.

Check

Divide 7 by 3 on a calculator: 7 ÷ 3 = 2.3333333333… which matches 2.333….

Similar repeating decimals

DecimalFraction
2.111…19/9
2.1666…13/6
2.222…20/9
2.444…22/9
2.5333…38/15
2.555…23/9
2.666…8/3
2.777…25/9

See also: 7/3 as a mixed number.

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