Percentage is ok for sizing images in responsive web pages, but is not very good for text. E.g. Say that you want a menu bar on the left that needs to be 240px wide, and you want to accommodate overall display widths from 480px to 960px. A percentage of 50% is needed to accommodate the menu bar at the minimum, but that wastes 240px at the maximum.
Using "position: absolute" you can set the menu bar width irrespective of the overall display width. Alternatively, using media-specific style sheets can minimise that problem, and are pretty well essential if you need to support displays less than 480px wide.