Question

Accuracy of measurement is determined by:
(A) Absolute error
(B) Percentage error
(C) Both
(D) None of these

Answer 1

Hint:By accuracy of measurement, we mean how close the measured values are to the correct or actual value. To know which of the given options determine accuracy we need to check which gives information of how much the measured value changes with respect to the correct value.

Complete step by step solution:
Let $$x$$be the actual length of the object and the measured length is $$x_m$$.Absolute error is defined as the difference between the measured value and its actual value of a quantity. So the absolute error will be equal to the difference between measured value and actual value or $$\mathrm{\Delta }x=x_m-x$$.
Percentage error is defined as the difference between the measured value and the actual value in comparison with the actual value. So the percentage error will be
Percentage error $$=\left|{\displaystyle \frac{\text{Measured value}-\text{Actual value}}{\text{Actual value}}}\right|\times 100$$
or Percentage error$$=\left|{\displaystyle \frac{x_m-x}{x}}\right|\times 100$$
Here, we can see that in case of absolute error it does show how the measured value is changed with respect to the actual value. But in case of percentage error we see it gives us the information of how the measured value changes with respect to the actual value. As accuracy is defined as how close the measured value is to the actual value, so accuracy of measurement is determined by percentage error.

The correct answer will be option (B).

Note: If it was given precision of measurement which means how close the measurement is to another measurement. In that case the answer would be none of these, as absolute error and percentage determines changes from its actual value.