A physical parameter a can be determined by measuring the parameters b, c, d and e using the relation a = \(b^{\alpha} c^{\beta} / d^{\gamma} e^{\delta}\) . If the maximum errors in the measurement of b, c, d and e are b_{1} %, C_1 %, d_{1} % and e^{1} %, then the maximum error in the value of a determined by the experiment is
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\(a = \frac{b^{\alpha} c^{\beta}}{d^{\gamma} e^{\delta}}\)
So maximum error in a is given by
\(\left(\frac{\Delta a}{a} \times 100 \right)_{\max} = \alpha \cdot \frac{\Delta b}{b} \times 100 + \beta \cdot \frac{\Delta c}{c} \times 100\)
\(+ \gamma \cdot \frac{\Delta d}{d} \times 100 + \delta \cdot \frac{\Delta e}{e} \times 100\)
\(= \left( \alpha b_{1} + \beta c_{1} + \gamma d_{1} + \delta e_{1} \right)\%\)
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