# Rounding vs Approximating

Mathematically, What is the difference between asking for the answer rounded and approximated?

i.e. If we have x = 2.4564, and we want x to the nearest two decimal places. What's the best way to ask? ... rounding your answer to the nearest two decimal places? or ... approximating your answer to the nearest two decimal places?

and which one is more common?

I've tried to search about it and didn't find any source talking about it.

For example, x=2.4564 is rounded to 2.46 with two decimal places, and $\frac {211} {90} = 2.455555...$ is an approximation of x within 0.2%.
In a sense, "rounding" is a very simple type of approximation. $2.456$ is an "approximation" of $2.4564$, but it is an approximation that was reached through a process of rounding.