Actually, the whole-number ratio turns one dot:
into four dots:
This preserves the aspect ratio perfectly.
As for projectors, there are three popular types of projectors: LCD, CRT, and DLP.
Both LCD and DLP have native resolutions. The LCD works like a laptop - you have an LCD screen with a back light. The only difference is that in a projector the backlight is much stronger, and focused through a lense.
DLP projectors are just wierd - it is actually a piece of silicon with a bunch of tiny mirrors that selectively reflect light. Odd, I know, but home theater enthusiasts prefer this to LCD's because of increased contrast, and the elimination of the pixelation caused by LCD's.
I personally own an LCD projector for my home theater - I hightly recommend them, but you do have to worry about the whole native resolution thing.
Check out www.projectorcentral.com
for more info.