Round integer division

Is it documented anywhere that floating-point numbers round
"scientifically", that is 0.5 rounds to the nearest even number? Compare:

SELECT round(2.5::real), round(2.5::numeric), round(3.5::real),
round(3.5::numeric);

generates

2 | 3 | 4 | 4

I stumbled across this when I was trying to use round(a::real/b::real)
to generate a rounded result to dividing integers, and noticed sometimes
0.5 was truncated and sometimes it was rounded up. Couldn't find
anything about this in the archives or the data type documentation. Is
there something obvious that I'm I missing?

Thanks,

--

Lee Hachadoorian
PhD Student, Geography
Program in Earth & Environmental Sciences
CUNY Graduate Center