Question

if the percentage error t a,b,c and d is given by 2%,4%,1%,3% respectively, and Z a2b/cd, than the percentage error in Z is given by
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Answer 1

Answer:

12% is the percentage error in the Z

Answer 2

Answer:

The percentage error in z is equal to ±12%.

Explanation:

Given, The percentage error of a,  Δa/a = 2%

Percentage error of b is Δb/b = 4%

Percentage error of c is given Δc/c = 1%

Percentage error of d ids given Δd/d = 3%

Now given the value of z,  $z=\frac{a^{2}b}{cd}$

Because z is given in the terms of a, b, c and d. So, we can use the percentage error of a, b, c and d to find the percentage error in z.

Percentage error of z is given by:

$\frac{\triangle z}{z}*100 \%=\pm [ 2\frac{\triangle a}{a}+\frac{\triangle b}{b}+\frac{\triangle c}{c}+\frac{\triangle d}{d}]$

$\frac{\triangle z}{z}*100\%=\pm[2(2\%)+4\%+1\%+3\%]$

$\frac{\triangle z}{z}*100\%=\pm[4\%+4\%+1\%+3\%]$

$\frac{\triangle z}{z}*100\%=\pm12\%$

Therefore, the percentage error in z will be equal to  ±12%.