0.303030… as a Fraction

0.303030… (0.30 repeating) as a fraction is 10/33.

How to convert 0.303030… to a fraction

  1. Let x = 0.303030... (the underlined part, 30, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 30.303030...
  3. Subtract to cancel the repeating tail: 100x − x = 30 − 0, so 99x = 30.
  4. Solve: x = 30/99. The greatest common divisor is 3, so x = 10/33.

Check

Divide 10 by 33 on a calculator: 10 ÷ 33 = 0.303030303… which matches 0.303030….

Similar repeating decimals

DecimalFraction
0.282828…28/99
0.285285285…95/333
0.2888…13/45
0.292929…29/99
0.307307307…307/999
0.3111…14/45
0.313131…31/99
0.3222…29/90

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