\begin{definition}[Definition:Rounding/Treatment of Half]
Let $n \in \Z$ be an integer.
Let $x \in \R$ be a real number.
Consider the situation when $\dfrac x {10^n} + \dfrac 1 2$ is an integer.
That is, $\dfrac x {10^n}$ is exactly midway between the two integers $\dfrac x {10^n} - \dfrac 1 2$ and $\dfrac x {10^n} + \dfrac 1 2$.
Recall that the general philosophy of the process of rounding is to find the closest approximation to $x$ to a given power of $10$.
Thus there are two equally valid such approximations:
:$\dfrac x {10^n} - \dfrac 1 2$ and $\dfrac x {10^n} + \dfrac 1 2$
between which $\dfrac x {10^n}$ is exactly midway.
There are a number of conventions which determine which is to be used.
\end{definition}