A physical quantity x is given by x = `(a^(2)b^(3))/(csqrtd)` . If the percentage errors of measurement in a, b, c and d are 4%, 2%, 3% and 1% respectively, then calulate the percentage error in the calculation of x.

Explanation

Given x = `(a^(2)b^(3))/(csqrtd)`
The percentage error in x is given by
`(Deltax)/(x) xx 100 = 2 (Deltaa)/(a) xx 100 + 3(Deltab)/(b) xx 100 + (Deltac)/(c) xx 100 + 1/2 (Deltad)/(d) xx 100`
= `(2xx4%)+(3xx2%)+(1xx3%)+(1//2xx1%)`
= `8% + 6% + 3% + 0.5%`
The percentage error is x = `17.5%`