How do computers and calculators use numerical methods?

Answer 1

Calculators don't. Computers on the other hand can use various different software that follow mathematical command lines that signify to the software program what it has to do to the date following the command. Using these commands correctly you can build algorithms of numerical methods which then solve the continuous mathematical problem for you instead of having to do it by hand.

This is incredibly beneficial when you get into more complex algorithms in more complex continuous mathematics. For example solving fixed-point iterations are relatively simple for normal equations. However for systems of equations it gets rather more complex and it is much simpler to write an algorithm for a computer to solve the problem, rather than try to do all the calculations by hand.