6.333… as a Fraction

6.333… (6.3 repeating) as a fraction is 19/3. As a mixed number that is 6 1/3.

How to convert 6.333… to a fraction

  1. Let x = 6.333... (the underlined part, 3, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 63.333...
  3. Subtract to cancel the repeating tail: 10x − x = 63 − 6, so 9x = 57.
  4. Solve: x = 57/9. The greatest common divisor is 3, so x = 19/3.

Since 19 is larger than 3, it can also be written as the mixed number 6 1/3.

Check

Divide 19 by 3 on a calculator: 19 ÷ 3 = 6.3333333333… which matches 6.333….

Similar repeating decimals

DecimalFraction
5.777…52/9
5.888…53/9
6.111…55/9
6.222…56/9
6.444…58/9
6.555…59/9
6.666…20/3
6.777…61/9

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