# Category:Definitions/Rounding

This category contains definitions related to Rounding.

Related results can be found in Category: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**.

## Pages in category "Definitions/Rounding"

The following 12 pages are in this category, out of 12 total.

### R

- Definition:Rounding
- Definition:Rounding Down
- Definition:Rounding to Even
- Definition:Rounding to Nearest Integer
- Definition:Rounding Up
- Definition:Rounding/Integer
- Definition:Rounding/Treatment of Half
- Definition:Rounding/Treatment of Half/Round Down
- Definition:Rounding/Treatment of Half/Round to Even
- Definition:Rounding/Treatment of Half/Round Up