First slide

Accuracy; precision of instruments and errors in measurements

Question

If X = a + b, the maximum percentage error in the measurement of X will be

Moderate

A

$(\frac{Δ a}{a} + \frac{Δ b}{b}) \times 100 %$
B

$(\frac{Δ a}{a + b} - \frac{Δ b}{a + b}) \times 100 %$
C

$(\frac{Δ a}{a + b} + \frac{Δ b}{a + b}) \times 100 %$
D

$(\frac{Δ a}{a} \times \frac{Δ b}{b}) \times 100 %$

Solution

$\begin{array}{l} X = a + b \Rightarrow Δ X = Δ a + Δ b \\ Now \frac{Δ X}{X} \times 100 = \frac{(Δ a + Δ b)}{a + b} \times 100 \\ = (\frac{Δ a}{a + b} + \frac{Δ b}{a + b}) \times 100 \end{array}$

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