If x = (a)/(b), then& the maximum relative error in the measurement...

x = \dfrac{a}{b},

then& the maximum relative error in the measurement is

Options

A $\dfrac{\dfrac{∆ a}{a}}{\dfrac{∆ b}{b}}$
B $\dfrac{\Deltaa}{a} + \dfrac{\Deltab}{b}$
C $\dfrac{\Deltaa}{a} - \dfrac{\Deltab}{b}$
D $\dfrac{\dfrac{∆ b}{b}}{\dfrac{∆ a}{a}}$

Correct answer

B. $\dfrac{\Deltaa}{a} + \dfrac{\Deltab}{b}$

Step-by-step solution

Given:& $x = \dfrac{a}{b}$
The relative error is expressed as the ratio between the measurement's absolute error and the actual measurement.
The expression for relative error is,~
Relativeerror = \dfrac{Meanabsoluteerror}{Actualvalue} $.</p><p>The maximum absolute error is given as for~$ a $~is~$ \Deltaa $~and for$ b $~is~$ \Deltab $.</p><p>Thus, the relative error is,$ \dfrac{\Deltaa}{a} + \dfrac{\Deltab}{b}.

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