0.345345345… as a Fraction

0.345345345… (0.345 repeating) as a fraction is 115/333.

How to convert 0.345345345… to a fraction

  1. Let x = 0.345345345... (the underlined part, 345, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 345.345345345...
  3. Subtract to cancel the repeating tail: 1000x − x = 345 − 0, so 999x = 345.
  4. Solve: x = 345/999. The greatest common divisor is 3, so x = 115/333.

Check

Divide 115 by 333 on a calculator: 115 ÷ 333 = 0.3453453453… which matches 0.345345345….

Similar repeating decimals

DecimalFraction
0.323232…32/99
0.333…1/3
0.343434…34/99
0.3444…31/90
0.353535…35/99
0.3555…16/45
0.363636…4/11
0.3666…11/30

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