0.494949… as a Fraction

0.494949… (0.49 repeating) as a fraction is 49/99.

How to convert 0.494949… to a fraction

  1. Let x = 0.494949... (the underlined part, 49, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 49.494949...
  3. Subtract to cancel the repeating tail: 100x − x = 49 − 0, so 99x = 49.
  4. Solve: x = 49/99. The greatest common divisor is 1, so x = 49/99 (already in lowest terms).

Check

Divide 49 by 99 on a calculator: 49 ÷ 99 = 0.4949494949… which matches 0.494949….

Similar repeating decimals

DecimalFraction
0.474747…47/99
0.4777…43/90
0.484848…16/33
0.4888…22/45
0.505050…50/99
0.5111…23/45
0.515151…17/33
0.5222…47/90

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