0.292929… as a Fraction

0.292929… (0.29 repeating) as a fraction is 29/99.

How to convert 0.292929… to a fraction

  1. Let x = 0.292929... (the underlined part, 29, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 29.292929...
  3. Subtract to cancel the repeating tail: 100x − x = 29 − 0, so 99x = 29.
  4. Solve: x = 29/99. The greatest common divisor is 1, so x = 29/99 (already in lowest terms).

Check

Divide 29 by 99 on a calculator: 29 ÷ 99 = 0.2929292929… which matches 0.292929….

Similar repeating decimals

DecimalFraction
0.272727…3/11
0.2777…5/18
0.282828…28/99
0.285285285…95/333
0.2888…13/45
0.303030…10/33
0.307307307…307/999
0.3111…14/45

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