5.333… as a Fraction

5.333… (5.3 repeating) as a fraction is 16/3. As a mixed number that is 5 1/3.

How to convert 5.333… to a fraction

  1. Let x = 5.333... (the underlined part, 3, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 53.333...
  3. Subtract to cancel the repeating tail: 10x − x = 53 − 5, so 9x = 48.
  4. Solve: x = 48/9. The greatest common divisor is 3, so x = 16/3.

Since 16 is larger than 3, it can also be written as the mixed number 5 1/3.

Check

Divide 16 by 3 on a calculator: 16 ÷ 3 = 5.3333333333… which matches 5.333….

Similar repeating decimals

DecimalFraction
4.777…43/9
4.888…44/9
5.111…46/9
5.222…47/9
5.444…49/9
5.555…50/9
5.666…17/3
5.777…52/9

See also: 16/3 as a mixed number.

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