If you are using the services of a professioanl printer, at least this is true for the printer that I use; there is DPI information in the image's header that tell the presses how to interpret the size of the image.
In other words, if I take a 3000x1500 image @ 100 dpi to the printer, I get a 30"x15" print back (and it looks very bad). The same image @ 300DPI, and I get a 10 X 5 print back (that looks about like it's supposed to).
And I have to use CYMK colors too, instead of RGB.
Could be different for other printers, don't know for sure.

DPI is completely irrelevant for web graphics or monitor display. Normal web graphics are 72, sometimes 96, DPI. It's all about image resolution (total pixels) divided by screen size in that case, the PPI.

Friends don't let friends use booleans.