FDM printers don't print in Dots, they print with a thread. The theoretical resolution on my printer is 160 steps per millimeter, so that would pe a pretty high DPI number. But since the thread is 0.4 mm thick, details finer than that aren't really possible. 

The Z axis (up/down) cannot be ultimatively thin, since the thread has to be squeezed to the layer height. My usual print size is 0.2 mm per layer, but I can go down to 0.05 mm layer, wich takes 4 times more time to print.

If you're planning to do smaller prints and you look for a good surface quality, I would suggest you look for an resin printer like the B9Creator or the Form1 from Formlabs. The print material is more expensive, but the priciple (UV hardening resins) are better for smaller prints.

In short, I cannot give an DPI value. It depends on the material, too.

 

A ship in port is safe; but that is not what ships are built for.
Sail out to sea and do new things.
-"Amazing Grace" Hopper

Avatar image of me done by Chidori.