I'm thinking (by now quite strongly) that there is a place
in "Introduction to R" (and maybe other basic documentation)
for an account of arithmetic precision in R (and in digital
computation generally).
A section "Arithmetic Precision in R" near the beginning
would alert people to this issue (there is nothing about it in
"Introduction to R", "R Language Definition", or "R internals").
Once upon a time, poeple who did arithmetic knew about this
from hands-on experience (just when do you break out of the
loop when you are dividing 1 by 3 on a sheet of paper?) -- but
now people press buttons on black boxes, and when they find
that 1/3 calculated in two "mathematically equivalent" ways
comes out with two different values, they believe that there
is a bug in the software.