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

As `P=(a^(3) b^(2))/((sqrt(c)d))=a^(3) b^(2)c^(-1//2)d^(-1)`
`:.` Maximum fractional error in the measurement
`(Delta P)/(P)=3 (Delta a)/a+2(Delta b)/(b)+1/2 (Delta c)/(c)+(Delta d)/d`
As `(Delta a)/a=1 %, (Delta b)/b=3 %, (Delta c)/c=4%` and `(Delta d)/d=2%`
`:.` Maximum fractional error in the measurement
`(Delta P)/P=3xx1%+2xx3%+1/2xx4%+2%`
`=3 %+6 %+2 %+2 %=13 %`
If `P=3.763`, then `Delta P= 13%` of `P`
`=(13 P)/100=(13xx3.763)/100=0.489`
As the error lies in first decimal place, the answer should be round off to first decimal place. Hence, we shall express the value of P after rounding it off as `P=3.8` .