\begin{definition}[Definition:Rounding/Treatment of Half/Round Down]
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 $\dfrac x {10^n} + \dfrac 1 2$.
The '''round down''' convention is that the '''smaller''' of those two integers is used:
:$y = 10^n \ceiling {\dfrac x {10^n} - \dfrac 1 2}$
where $y$ is the rounded value.
\end{definition}