Definition:Numerical Analysis/Motivation

Numerical Analysis: Motivation

It is impossible to write down an exact decimal representation of a solution to certain equations, as they may be irrational.

Certain other problems are defined by equations which cannot be solved using analytical methods.

Hence:

The aim of numerical methods is to provide practical procedures for calculating the solutions of problems in applied mathematics to a specified degree of accuracy.
-- B. Noble: Numerical Methods: Volume $\text { 1 }$

To produce a number which answers a problem is only one aspect of the topic of numerical analysis.

The other aspect, usually more difficult, is to ensure that the answer is correct within particular stated limits.