A physical quantity P is related to four observables a, b, c and d as follows:
P = `(a^(3)b^(3))/(sqrt(cd))`
The percentage errors of measurement in a,b, c and d are 1%, 3%, 4%, and 2% respectively. What is the percentage error in the quantity P? If the value of P calculated using the given relation turns out to be 3.763, to what value should the result be rounded off?

Explanation

`P=(a^(3)b^(2))/(sqrtcd)=(a^(3)b^(2))/(c^(1//2)d)`
So the errors are related as
`(DeltaP)/(P)=3(Deltaa)/(a) +2(Deltab)/(b)+(1)/(2)(Deltac)/(c)+(Deltad)/(d)`
Putting the given values,
`(DeltaP)/(P)=3xx(1)/(100)+2xx(3)/(100)+(1)/(2)xx(4)/(100)+(2)/(100)=(13)/(100)`
Therefore percentage error in P = 13%
As the relative error 0.13 has 2 significant digits it is useless to keep the subsequent digits. So the calculated value of P should reasonably be rounded off as `P = 3.763 ~~3.8`