The general convention in engineering is that any dimension expressed in decimal fractions (1.750" for example) is one that expected to be made to a tolerance of 1/2 thou either way - so 1.750" really means between 1.7495" and 1.7505". That level of precision - or even tighter, sometimes - may be necessary to ensure proper fits between components. Dimensions expressed in fractions (7/8" for example) are not expected to be so precise. Both methods may be used on the same drawing in some instances.

In woodwork, the precision implied by using decimal fractions is not really appropriate. After all, wood shrinks and swells with different levels of humidity, so a piece that may be 1.750" thick at 10 o'clock in the morning may be 1.753" by 2 o'clock in the afternoon if it happens to have started raining! By the same token, if you want 1/4" mortices, your mortice chisel may well not be exactly 0.250" wide. It's actual width doesn't matter one jot as long as it's about 1/4", because you'll cut the tenons to fit. So specifying 1/4" on the drawing is plenty close enough.

Another factor to take into account is what measuring equipment the person reading the drawing will have available. Most tape measures have metric dimensions in metres and millimetres, and imperial in feet, inches and fractions of an inch - 1/4's, 1/8's 1/16's are the usual ones - so it would be sensible to use these instead of decimal fractions of an inch, which would require the workman to make a conversion to something actually on his tape. He can read off 16 7/8", but 16.875" would make him scratch his head. The less chance of errors arising by having to make mental conversions, the better.