A quantity Q is formulated as , and Z are independent parameters which have fractional errors of 0.1, 0.2 and 0.5, respectively in measurement. The maximum fractional error of Q is [2025]

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Solution

Q.
A quantity Q is formulated as $X^{- 2} Y^{+ \frac{3}{2}} Z^{- \frac{2}{5}} \cdot X, Y$ , and Z are independent parameters which have fractional errors of 0.1, 0.2 and 0.5, respectively in measurement. The maximum fractional error of Q is [2025]

1 0.1

2 0.8

3 0.7

4 0.6

Ans.
(3)

Fractional error $= 2 \frac{△ X}{X} + \frac{3}{2} \frac{△ Y}{Y} + \frac{2}{5} \frac{△ Z}{Z}$

$= 2 (0.1) + \frac{3}{2} (0.2) + \frac{2}{5} (0.5)$

= 0.2 + 0.3 + 0.2 = 0.7

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