Tim's link points out difference of PPI vs. DPI. As he stated, "dpi stands for dots per inch, and it's a physical measure of how many dots go on a piece of paper. We don't care about this. The output device could be a continuous tone printer, a 250dpi minilab, or a 4000dpi inkjet, we just don't care."
To illustrate this point, the embedded value in EXIF might have '72 dpi', I can print it on a Canon printer which assumes 300 dpi, or an Epson printer which assumes 360 dpi, and never have touched my actual photo file to change the EXIF value which is embedded into the file!
Furthermore, I might use a Canon ip100 printer whose head and paper advance is capable of 9600 x2400 dpi per its specifications, while I might also use a Canon iP2702 printer whose head and paper advance is capable of 4800 x1200 dpi per its specifications and never have touched my actual photo file to change the EXIF value which is embedded into the file!
DPI specification is that irrelevant. DPI came about as an output device specification in the days before digital photography, as an offset print setting for 'screen' mesh size, which affected the quality of printed photos on pages like newspaper (low DPI) vs. glossy magazines like National Geographic (high DPI).
One complication to this is the fact that often we use software which calls it 'DPI' (wrongly) when the software is deterimining 'PPI' (Pixels Per Inch) in its export of JPG from RAW conversion, as the total pixel count is determine by the product of print size x 'DPI'...a 5184x3456 pixel 7D photo intended to print a 4x6" photo at 200 ppi has '200 DPI' as the output parameter (not PPI) in some software, and the software outputs a JPG file of 800x1200 pixels as a result...which is '200 PPI' in the final print, not '200 DPI'. And pro labs often repeat this same confusing error because their software is similarly AFU.
Lastly, let me comment that I often use Zoombrowser to do 4x6" printing on my home printer with a 3888x2592 pixel (40D) file, using a file with 72 dpi embedded into its EXIF, and I also might send that same file to Costco for printing 8x10" with the same 72 dpi value in the EXIF, and I get the right sized output and never touched the embedded EXIF value. Nor have I changed the file's pixel sizing (from 1200x1800 to 2400x3000, to keep a 300 DPI or 300 PPI output in the 4x6 or 8x10, respectively). The only time I bother with counting pixels is if I want to have a large print made (e.g. 16x20") and then I resize the file to 4800x6000 pixels in order to meet the lab's 300 PPI minimum (although they might wrongly state it as a '300 DPI minimum' 