Write a note on the combination of errors.

(N/A) When an experiment involves several measurements,the errors in all individual measurements combine to affect the final result.
For example,in the measurement of density $(d = m/V)$,the errors in the measurement of mass $(m)$ and volume $(V)$ will combine to produce an error in the calculated density.
Errors combine according to the following mathematical operations:
$1$. Addition: If $z = a + b$,then the absolute error $\Delta z = \Delta a + \Delta b$.
$2$. Subtraction: If $z = a - b$,then the absolute error $\Delta z = \Delta a + \Delta b$.
$3$. Multiplication: If $z = ab$,then the relative error $\frac{\Delta z}{z} = \frac{\Delta a}{a} + \frac{\Delta b}{b}$.
$4$. Division: If $z = a/b$,then the relative error $\frac{\Delta z}{z} = \frac{\Delta a}{a} + \frac{\Delta b}{b}$.
$5$. Power: If $z = a^n$,then the relative error $\frac{\Delta z}{z} = n \frac{\Delta a}{a}$.