\begin{definition}[Definition:Rounding]
'''Rounding''' is the process of approximation of a value of a variable to a multiple of a given power of whatever number base one is working in (usually decimal).
Let $n \in \Z$ be an integer.
Let $x \in \R$ be a real number.
Let $y \in \R$ such that:
:$y = 10^n \floor {\dfrac x {10^n} + \dfrac 1 2}$
or:
:$y = 10^n \ceiling {\dfrac x {10^n} - \dfrac 1 2}$
where $\floor {\, \cdot \,}$ denotes the floor function and $\ceiling {\, \cdot \,}$ denotes the ceiling function.
Then $y$ is defined as '''$x$ rounded to the nearest $n$th power of $10$'''.
Both of these definitions amount to the same thing, except for when $\dfrac x {10^n}$ is exactly halfway between $\floor {\dfrac x {10^n} }$ and $\ceiling {\dfrac x {10^n} }$.
How these instances is treated is known as the '''treatment of the half'''.
\end{definition}