The percentage errors of measurement in a, b, c and d are 1%. 3%, 4% and respectively. What is the percentage error in the quantity P? If the value of P calculated using the above relation turns out to be 3.763, to what value should you round off 2% the result? e resuuiit

Explanation

Here, `P =(a^3 b^2)/(sqrtc d)`
Maximum fractional error in P is given by
`(Delta P)/(P) = +-[3(Delta a)/(a) +(Deltab)/(b) +(1)/(2) (Deltac)/(c ) +(Deltad)/(d)] = +-[ 2((1)/(100))+2((3)/(100))+(1)/(2)((4)/(100))+(2)/(100)] = +- (13)/(100) =+-0.13`
`"Percentage error in" P = (DeltaP)/(P)xx100 = +- 0.13xx100 = +- 13%`
As the result (13%error) has two significant figures, therefore, if P turns out to be 3.763, the result would
be rounded off to 3.8.