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A physical quantity z depends on four observables a, b, c and d, as $z = (a^{2}b^{2/3})/(\sqrt{c} d^{3})$. The percentages of error in the measurement of a, b, c and d are 2%, 1.5%, 4% and 2.5% respectively. The percentage of error in z is:
Explanation
Given: $Z = a^{2}b^{2/3}/(\sqrt{c} d^{3})$ Percentage error in Z, $\Delta Z/Z = 2\Delta a/a + (2/3)(\Delta b/b) + (1/2)(\Delta c/c) + 3(\Delta d/d)$ = $2 \times 2 + (2/3) \times 1.5 + (1/2) \times 4 + 3 \times 2.5 = 14.5\%$.