3.1416 and 3.14160 are exactly the same number.
Well, perhaps they are-- and perhaps they are not. It's ambiguous without additional information.
As a scientist, though, I have to say that I think that the practice of teaching children to ASSUME infinite trailing zeros is probably unsound, at least when looking at the larger picture, but thanks for the burnt toast aside. The non-theoretical universe seems to be primarily composed of burnt toast, ethanol, and mateless socks, by the way.
The vast majority of students (future psychiatrists, attorneys, deputies, teachers, and yes, engineers, scientists and physicians) might be better served to have a clear and intuitive understanding that
measured values are
not infinitely precise. That's my opinion, but I guess we're each sharing our biases freely at this point. It's easier to explain "the value is exact-- assume an infinite number of significant figures" than to try to explain things the other way round-- for students, I mean.
Clearly math pedagogy concerns itself with such things. Why else would one bother teaching students about significant figures to begin with? The assumption that 3.67 is numerically identical to 3.67000000 means that the idea of significant figures is somewhat extraneous as a math concept to begin with. It
is an assumption. Why assume that particular thing rather than something else?
Why teach the topic of significant figures at all if such a thing
should be unilaterally assumed in math?
