Relative Error $\frac{x-x_0}{x}$

Question

According to many definitions I've seen the relative error is defined by

$$E = \frac{x-x_0}{x}$$ where $x$ is the "true" value. But some people use instead $$\frac{x-x_0}{x_0}. $$ Is this incorrect?

Answer 1

Let $\Delta x$ be the absolute error. Then $\Delta x=x_0-x$ where $x$ is true value and $x_0$ is measured value (sometimes with the absolute value taken). Relative error $\delta x$ is defined by $$\delta x=\dfrac{\Delta x}{x}=\dfrac{x_0-x}{x}$$