A physical quantity A is related to four observables a, b. c and d as follows A = a2b3cd. The percentage errors of measurement in a, b, c and d are 1%, 3%, 2% and 2% respectively. What is the percentage error in the quantity A?

A=a2b3cd⇒∆AA=2∆aa+3∆bb+∆cc+12∆dd= 2(1) + 3(3) + 2 + 12 (2)= 14%

A physical quantity A is related to four observables a, b. c and d as follows A = a2b3cd. The percentage errors of measurement in a, b, c and d are 1%, 3%, 2% and 2% respectively. What is the percentage error in the quantity A?

A=a2b3cd⇒∆AA=2∆aa+3∆bb+∆cc+12∆dd= 2(1) + 3(3) + 2 + 12 (2)= 14%

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A physical quantity A is related to four observables a, b. c and d as follows $A = \frac{a^{2} b^{3}}{c \sqrt{d}}$ . The percentage errors of measurement in a, b, c and d are 1%, 3%, 2% and 2% respectively. What is the percentage error in the quantity A?

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$A = \frac{a^{2} b^{3}}{c \sqrt{d}} \Rightarrow \frac{∆ A}{A} = 2 \frac{∆ a}{a} + 3 \frac{∆ b}{b} + \frac{∆ c}{c} + \frac{1}{2} \frac{∆ d}{d}$
= 2(1) + 3(3) + 2 + $\frac{1}{2}$ (2)= 14%

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A physical quantity A is related to four observables a, b. c and d as follows A = a2b3cd. The percentage errors of measurement in a, b, c and d are 1%, 3%, 2% and 2% respectively. What is the percentage error in the quantity A?

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A physical quantity A is related to four observables a, b. c and d as follows $A = \frac{a^{2} b^{3}}{c \sqrt{d}}$ . The percentage errors of measurement in a, b, c and d are 1%, 3%, 2% and 2% respectively. What is the percentage error in the quantity A?