Definition:Rounding/Treatment of Half/Round Down

Definition
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:


 * $X = 10^n \ceiling {\dfrac x {10^n} - \dfrac 1 2}$

where $X$ is the rounded value.