"Why is accurate measuring and that fraction of an inch so important to you? "
It's something that stays with us from doing subjects like technical drawing at school.
Most of the measurements here don't split into fractions of less than a half as far as I've seen.There are a few extremists who talk about quarters of an inch but I think if a guy is happy with the number of whole inches he has then he's less likely to be concerned with fractions.