Chapter 2 - Derivatives - 2.9 Linear Approximations and Differentials - 2.9 Exercises - Page 193: 37

$\frac{ΔI}{I}$ $\approx$ $-\frac{dR}{R}$

$V$ = $IR$ $I$ = $\frac{V}{R}$ $dI$ = $-\frac{V}{R^{2}}dR$ The relative error in calculating $I$ is $\frac{ΔI}{I}$ $\approx$ $\frac{dI}{I}$ = $\frac{-\frac{V}{R^{2}}dR}{\frac{V}{R}}$ = $-\frac{dR}{R}$ so the relative error in calculating $I$ is approximately the same (in magnitude) as the relative error in $R$