1.333… as a Fraction

1.333… (1.3 repeating) as a fraction is 4/3. As a mixed number that is 1 1/3.

How to convert 1.333… to a fraction

  1. Let x = 1.333... (the underlined part, 3, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 13.333...
  3. Subtract to cancel the repeating tail: 10x − x = 13 − 1, so 9x = 12.
  4. Solve: x = 12/9. The greatest common divisor is 3, so x = 4/3.

Since 4 is larger than 3, it can also be written as the mixed number 1 1/3.

Check

Divide 4 by 3 on a calculator: 4 ÷ 3 = 1.3333333333… which matches 1.333….

Similar repeating decimals

DecimalFraction
0.9888…89/90
0.989898…98/99
1.111…10/9
1.1666…7/6
1.222…11/9
1.444…13/9
1.555…14/9
1.666…5/3

See also: 4/3 as a mixed number.

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