7.333… as a Fraction

7.333… (7.3 repeating) as a fraction is 22/3. As a mixed number that is 7 1/3.

How to convert 7.333… to a fraction

  1. Let x = 7.333... (the underlined part, 3, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 73.333...
  3. Subtract to cancel the repeating tail: 10x − x = 73 − 7, so 9x = 66.
  4. Solve: x = 66/9. The greatest common divisor is 3, so x = 22/3.

Since 22 is larger than 3, it can also be written as the mixed number 7 1/3.

Check

Divide 22 by 3 on a calculator: 22 ÷ 3 = 7.3333333333… which matches 7.333….

Similar repeating decimals

DecimalFraction
6.777…61/9
6.888…62/9
7.111…64/9
7.222…65/9
7.444…67/9
7.555…68/9
7.666…23/3
7.777…70/9

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