3.333… as a Fraction

3.333… (3.3 repeating) as a fraction is 10/3. As a mixed number that is 3 1/3.

How to convert 3.333… to a fraction

  1. Let x = 3.333... (the underlined part, 3, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 33.333...
  3. Subtract to cancel the repeating tail: 10x − x = 33 − 3, so 9x = 30.
  4. Solve: x = 30/9. The greatest common divisor is 3, so x = 10/3.

Since 10 is larger than 3, it can also be written as the mixed number 3 1/3.

Check

Divide 10 by 3 on a calculator: 10 ÷ 3 = 3.3333333333… which matches 3.333….

Similar repeating decimals

DecimalFraction
2.888…26/9
3.111…28/9
3.222…29/9
3.444…31/9
3.555…32/9
3.666…11/3
3.777…34/9
3.8333…23/6

See also: 10/3 as a mixed number.

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