Approximations in mathematics is simply the idea or concept of taking the closest number to a given real value. For example, 2,100 is approximately 2,000. 

This is sometimes helpful in writing the numbers in a more comprehensive (in the case of whole numbers) or shorter (in the case of decimals) way.

Approximations are done by "rounding off" certain numbers according to precise rules. Rounding off could either be rounding down or rounding up.