0.333… as a Fraction

0.333… (0.3 repeating) as a fraction is 1/3.

How to convert 0.333… to a fraction

  1. Let x = 0.333... (the underlined part, 3, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 3.333...
  3. Subtract to cancel the repeating tail: 10x − x = 3 − 0, so 9x = 3.
  4. Solve: x = 3/9. The greatest common divisor is 3, so x = 1/3.

Check

Divide 1 by 3 on a calculator: 1 ÷ 3 = 0.3333333333… which matches 0.333….

Similar repeating decimals

DecimalFraction
0.3111…14/45
0.313131…31/99
0.3222…29/90
0.323232…32/99
0.343434…34/99
0.3444…31/90
0.345345345…115/333
0.353535…35/99

See also: 1/3 as a decimal.

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