For a physical quantity defined as

PHYSICS · Single correct · A Level · Physics · Measurements and their errors · Measurements and their errors

Problem

For a physical quantity

z

defined as

z = x^{n}

, which one of the following gives the fractional uncertainty

\dfrac{\Delta z}{z}

in terms of the fractional uncertainty of

x

? (a)

\left(\dfrac{\Delta x}{x}\right)^{n}

(b)

|n|\,\dfrac{x}{\Delta x}

(c)

|n|\,\dfrac{\Delta x}{x}

(d)

n\,\dfrac{\Delta x}{x}