Definition:Relative Error/Also defined as

Definition

Let $x_0$ be an approximation to a (true) value $x$.

The relative error of $x_0$ in $x$ can also be defined as:

$\delta x \approx \dfrac {\Delta x} {x_0}$

where:

$\Delta x$ denotes the absolute error of $x_0$

$\approx$ indicates that the value is but approximate.

This can be particularly useful when the true value $x$ can only be speculated.

Sources

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of Mathematical Functions ... (previous) ... (next): $3$: Elementary Analytic Methods: $3.5$ Absolute and Relative Errors: $3.5.2$
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): relative error