Definition:Rounding

Definition
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:
 * $\dfrac y {10^n} = \left\lfloor{\dfrac x {10^n} + \dfrac 1 2}\right\rfloor$

Then $y$ is defined as $x$ rounded to the nearest $n$th power of $10$.

Rounding to Nearest Integer
When $n = 0$, the operation is referred to as rounding to the nearest integer:

Also known as
When $n < 0$, the terminology used is usually:


 * $x$ rounded to the nearest $m$th decimal place

where $m = -n$.