A physical quantity P is related to four observables a, b, c and d as `P=a^(3)b^(2)//sqrtcd`. The percentage errors in the measurements of 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 this formula turns out to be `3.763`, to what value should you round off the result?

Explanation

Relative error in P is given by
`(DeltaP)/(P)=3(Deltaa)/(a)+2(Deltab)/(b)+(1)/(2)(Deltac)/(c)+(Deltad)/(d)`
So, percentage error
`(DeltaP)/(P)xx100=3((Deltaa)/(a)xx100)+2((Deltab)/(b)xx100)+(1)/(2)((Deltac)/(c)xx100)+(Deltad)/(d)xx100`
`=(3xx1%)+(2xx3%)+((1)/(2)xx4%)+(1xx2%)`
`=13%`
Rounded off value of P = 3.8.