I need to describe upper and lower limits of an already rounded decimal numer.
4.7 using < or = to ?????
I gotta get this in tommrow or I'm grounded
Bionicle joe
The question is impossible to answer because we know nothing of how the number is generated, measured, etc. In order to do this we need to know something like a standard deviation or variance or something.
However, there is a convention which, though not particularly realistic, that answers your question depending on what class you are in. I note that the number 4.7 has two significant digits. The convention is, when no other information is given, that the least significant digit has an uncertainty of $\displaystyle \pm 1$. So I would say that 4.7 represents the interval between 4.6 and 4.8. Or in your notation:
$\displaystyle 4.6 \leq 4.7 \leq 4.8$
(This convention essentially comes from the idea that the number measured comes from rounding: 4.7 could be generated by, say, 4.651 all the way up to, say, 4.749, which is an interval of about 1 in the least significant digit. However note that you could equally well use this argument to show that the number 4.7 represents the interval from 4.6 to 4.7.)
-Dan