0.505050… as a Fraction

0.505050… (0.50 repeating) as a fraction is 50/99.

How to convert 0.505050… to a fraction

  1. Let x = 0.505050... (the underlined part, 50, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 50.505050...
  3. Subtract to cancel the repeating tail: 100x − x = 50 − 0, so 99x = 50.
  4. Solve: x = 50/99. The greatest common divisor is 1, so x = 50/99 (already in lowest terms).

Check

Divide 50 by 99 on a calculator: 50 ÷ 99 = 0.5050505051… which matches 0.505050….

Similar repeating decimals

DecimalFraction
0.4777…43/90
0.484848…16/33
0.4888…22/45
0.494949…49/99
0.5111…23/45
0.515151…17/33
0.5222…47/90
0.525252…52/99

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