Help interpreting DPI in scanners

I'm shopping for a new scanner. Some of them say that they scan at 1200 dpi (such as the one I currently have that isn't working well); one I'm looking at says it scans at 2400x4800 dpi.

So how to compare them? It seems a bit overboard, that the second one should be 11.5 million dpi (2400*4800). So how do I compare those numbers?

EDIT: Eliminated reference to the "square" of a number, as it was only a footnote.

 

On a CNET product page, I saw that the HP Scanjet 3500C is listed as 1200x1200; on the HP page itself, it is only listed as 1200 dpi. So I assume that 1200 really means 1200x1200 dpi.

So a Canon scanner listed at 2400x4800 would be much more than twice as clear as the ScanJet 3500C, then, correct?

 

Hi Paul, Here's a good explanation on scanning resolutions:http://www.dpreview.com/forums/thread/1788421
Takes a bit of reading and understanding. Neil.

 

You were given some good info in this thread that you started.

http://www.windowsbbs.com/pc-hardware/109223-scanner-recommendation.html