<p>I have a reprap printer with 0.3mm nozzle. It prints quite well, I am really surprised with quality of all the surfaces and the general precision of the parts printed. BUT I HAVE a problem: when making (for example) a 10mm x 10mm x 10mm cube with a 2.8mm diameter hole from top to bottom (to fit a screw) after I print it gets a size of 3mm diameter.</p>

<p>I know this is related to extrusion width but cant the slicer software (I am using s3d) know that it is using a specific extrusion width and compensate for that in order to get the diamter right?</p>

<p>OBS: this printer is supposed to get 0.05mm precision.</p>

It's a generally accepted fact that FDM/FFF printers will have
deviations when it comes to holes and perimeters
. Typically, holes print smaller than designed and external surfaces end up larger than designed.
In your case, it seems to be the opposite: the hole is too big. It could be that you're just printing too big overall. You might want to make sure that your printer is printing the 10mm X/Y dimension in you example correctly. If it's too big, part of it may be just the typical oversized perimeter, but some of it might be due to incorrect firmware X/Y 'steps/mm' or extrusion like you mentioned.
See also:
"Are you printing undersized holes?"