Define and give mathematical expression for absolute error, relative error and percentage error

Question Id: PH0000001

Question: Define and give mathematical expression for absolute error, relative error and percentage error.

Solution: 

Absolute Error: The difference between the measured or inferred value of a quantity and its actual value is called the absolute error ( $AE$ ). 

So, $AE=V_{a}-V_{e}$ 

Where $V_{a}$  is approximate value and $V_{e}$ is the exact value.

Relative Error: The ratio of the absolute error of the measurement to the actual measurement is called relative error ( $RE$ ).

So, $RE=\frac{AE}{V_{e}}=\left | \frac{V_{a}-V_{e}}{V_{e}} \right |$

Percent error($PE$) is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage. In other words, the percent error is the relative error multiplied by 100.

So, $PE=R_{e}\times 100%=^{}\frac{AE}{V_{e}}=\left | \frac{V_{a}-V_{e}}{V_{e}} \right |\times 100%$ 

∴ Above are the definition and mathematical expression . (Answer)

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