Question

The percentage errors in a, b and c are 1%,0.1% and 0.2% respectively.The maximum percentage error in a^2c/b will be​

Answer 1

Given,

The percentage errors in a= 1%, b = 0.1% and c = 0.2%

To Find,

The maximum percentage error in a²c/b

Solution,

To find the maximum error, we have to multiply the percentage error of each quantity with their respective power and add all of them.

Now,

Percentage error in a²c/b = 2*1 + 0.2 + 0.1

                                           = 2.3 %

Hence, the maximum percentage error in a²c/b is 2.3%.

Answer 2

Given:

Percentage error of a=1%

                                 b=0.1%

                                 c=0.2%

To Find:

Find the percentage error of expression x = a²×c/b

Solution:

Percentage error:

Percentage error is the difference between the experimental value of observation and theoretical value of the observation.It is usually given as a positive number and it is represented as in terms of percent.

For the expression x = a²×c/b , percentage error of x will be given as :

%error of x= 2×%error of a+%error of c+%error of b

we take only the mod value of the power of variables.

put the values, we get

%error of x= 2×1+0.1+0.2

                 =2.3%

Hence the percentage error of a²×c/b is 2.3%.