(First, irfanview might round of the size indication. Don't know the program, but it might show 7.5 as 8.)
dpi = dots per inch = pixels per inch. How many pixels are crammed into an inch of print.
Visual example here:
http://www.ransen.com/Articles/DPI/Default.htm(Ignore the abstraction of DPI and PPI in this link. Same-same.)
It is a value that ONLY comes into play when a picture needs to be translated into an actual print. It will not have relevance in terms of how it is presented on your screen.
(there are some disclaimers to that, but they are 99,9% not likely to have relevance here.)
There is two ways about it:
1) Crop the picture the way you would like to (in an aspect of 4 by 3 in this case). Take the width of the picture in pixels, divide it by ten (the ten inches). Thats the dpi the picture should be saved with in order for it to be 10 inches wide.
2) Decide on a dpi. Say 150. Multiply that by 10 and 7,5. That is now your pixel size of the image. 1500 x 1125. Resize the image to that size (make sure it is already in a 4x3 aspect, otherwise it will be stretched/squished).
Now attaining some of this might be problematic in any specific program. Let me know if you are stopped in this by something - and I'll try to help.