First slide

Accuracy; precision of instruments and errors in measurements

Question

An experiment measures quantities a, b, and c, and then X is calculated from $X = \frac{a^{1 / 2} b^{2}}{c^{3}}$ . If the percentage errors in a, b, and c are $\pm 1 %, \pm 3 %$ , and $\pm 2 %$ , respectively, then the maximum percentage error in X can be

Moderate

A

$\pm 12.5 %$
B

$\pm 7 %$
C

$\pm 1 %$
D

$\pm 4 %$

Solution

$\begin{array}{l} X = \frac{a^{1 / 2} b^{2}}{c^{3}} \\ \frac{ΔX}{X} \times 100 = \frac{1}{2} \frac{Δa}{a} \times 100 + 2 \frac{Δb}{b} \times 100 + 3 \frac{Δc}{c} \times 100 \\ = \frac{1}{2} \times 1 + 2 \times 3 + 3 \times 2 = 12 .5 % \end{array}$

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