Title: Percentage Error.

Objective:

At the end of this lesson, you will be able to calculate the percentage error of a measurement.

What you should know:

=> You should be familiar with finding the percentage of a value, that is, the percentage of a value is the same as

^Value/_{given percentage} * 100%.

=> Multiplication of fractions.

Introduction:

Percentage error is a means of determining the accuracy or the precision of a measurement compared to a known or expected value. Therefore, Percentage Error (P.E) = ^error/_{actual value} * 100%.

Presentation/ Step:

Ex 1. Given the measurement of an iron rod as 60cm with an error of 0.5, what is the P.E?

Step: Using the formula, Percentage Error (P.E) = ^error/_{actual value} * 100%.

=> P.E = ^0.5/₆₀ * 100% => 0.008333 * 100 = 0.8333

=> Therefore, the Percentage Error is 0.83% approx.

Ex 2. A cloth of length 2m was measured as 2.3m by a tailor. Calculate the percentage error in the tailor's measurement.

Step: Error from the measurement = 2.3m - 2m = 0.3m.

=> P.E = ^0.3m/_2.3m * 100% => 0.1304 * 100 = 13.043

=> Therefore, the Percentage Error is 13.04% approx.

Ex.3. A bag of cement weighs 50kg from the factory but the seller recorded the weight as 49.95 kg, calculated the percentage error.

Step: Error from the seller, 49.95 - 50kg = -0.05kg.

=> P.E = ^-0.05kg/_50kg * 100 => -0.001 * 100 = -0.1kg

=> Therefore, the Percentage Error is -0.1kg

Summary/ Conclusion:

=> In examples 1 and 2 the error values are positive because the measurements are in excess, while in example 3 error is a negative value because the measurement was not in excess.

Exercise:

The length of a plywood is measured by a carpenter as 60m. If the P.E. is ¹/₃%, what will be the actual length?