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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:

$y = 10^n \floor {\dfrac x {10^n} + \dfrac 1 2}$


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

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.