But that's exactly the point--historically, you wouldn't cut 3.93701 inches. You don't have the precision to do it nor do you have any real reason not to stick

But that's exactly the point--historically, you wouldn't cut 3.93701 inches. You don't have the precision to do it nor do you have any real reason not to stick with "round" numbers or close enough. Rough carpentry (e.g., framing a house) is often only accurate to a 1/2" or so; very fine furniture might go down to a 1/32rd. Note that machinists, who do want that sort of precision and can achieve it, mostly work in metric or metric-lite ('mils'=1/1000s of an inch).