.240 seems too small to me, a couple of thou under nominal should be fine.....BUT...this isn't that is going to determine thread fit. that is determined by how deep the V is which as Rick mentioned can be measured a couple of different ways.
if you look at the dies, they should be split, some of them have a screw. 90 degrees in each direction the split you'll likely find dimples in the die. you should have set screws in the die holder that engages these dimples; you literally control the fit of the thread by putting more or less pressure on these.
there are various classes of fit to threads you can read up on, but from using a commercial die and commercial tap an interference fit is not good. as you might imagine, for each fit there are different tolerances and clearances; fine tuning to get where you want is what those set screws are for
btw, measuring the thread can be useful when you are diagnosing problems or when single pointing, but more practically, you just make the male to the female. If you have a male thread that is too tight, chase with the die tightened up a little.