Question

Amy measured the density of copper as 7.2 x 10^3 kg/m^-3. Jamie measured it as 8.1 x 10^3 kg/m^-3.

a) Calculate the percent difference between the two measurements.

b) If the actual density of copper is 8.93 x 10^3 kg/m^-3, calculate the percent error in each of the measurement.

Answer 1

As we know that,

Density of the copper = 8930 kg/m3

And we have given that,

Amy measure of density of copper (Pa)= 7.2 x 10^3 kg/m^-3.

Jamie measure (Pj) = 8.1 x 10^3 kg/m^-3.

a) To Calculate the percent difference between the two measurements we have the relation as,

% difference = [|(Pa-Pj)|/(Pa+Pj)/2 ] × 100

Here we have to only consider the magnitude of the differences not there sign so mod is present there.

On substitution of values we will get,

% difference = (|7200-8100|)/(8100+7200)/2 × 100

% difference = 11.7647% difference

b) Now If the actual density of copper is 8.93 x 10^3 kg/m^-3, then to calculate the percent error in each of the measurement will be given as,

% error = (|E-T|/T) × 100

% error in Amy measurement will be,

% error ( in Amy) = 7200- 8930/8930 × 100

= 19.3729% error

Now % error ( in jamie) = (8100 - 8930/8930)×100

%error (in jamie) = 9.29451% error