0.343434… as a Fraction

0.343434… (0.34 repeating) as a fraction is 34/99.

How to convert 0.343434… to a fraction

  1. Let x = 0.343434... (the underlined part, 34, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 34.343434...
  3. Subtract to cancel the repeating tail: 100x − x = 34 − 0, so 99x = 34.
  4. Solve: x = 34/99. The greatest common divisor is 1, so x = 34/99 (already in lowest terms).

Check

Divide 34 by 99 on a calculator: 34 ÷ 99 = 0.3434343434… which matches 0.343434….

Similar repeating decimals

DecimalFraction
0.3222…29/90
0.323232…32/99
0.333…1/3
0.3444…31/90
0.345345345…115/333
0.353535…35/99
0.3555…16/45
0.363636…4/11

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