Errors in Measurement of Physical Quantities
Senior 2 · Physics
Errors in Measurement of Physical Quantities
Lesson 3 of 4
22 min
Let's begin
A trader's scale is uncertain by ±0.5 kg. On a 25 kg sack of maize flour, that hardly matters. On a 2 kg bag of sugar, the same ±0.5 kg is a quarter of the whole bag. To compare uncertainties fairly, you need to express them in three ways: absolute, relative and percentage.
A measuring cylinder reads 46 cm³ ± 1 cm³. Find the relative and percentage errors.
Relative error = 1 ÷ 46 = 0.022. Percentage error = 0.022 × 100% = 2.2%.
A bench is measured with a tape as 2.00 m ± 0.01 m. A pencil is measured with a ruler as 15.0 cm ± 0.1 cm. Which measurement is better?
The bench has the larger absolute error (1 cm against 1 mm), yet it is the better measurement, because its percentage error is smaller. Always compare uncertainties as percentages.
An S2 class measures the acceleration due to gravity as 9.6 m/s². The accepted value is 9.8 m/s². What is their percentage error?
Percentage error = |measured − accepted| ÷ accepted × 100% = 0.2 ÷ 9.8 × 100% = 2.0%.
Tip
Absolute has a unit. Relative and percentage do not
Do not forget the × 100% in a percentage error. If you stop at 0.022, you have given the relative error, not the percentage.
A digital balance shows 125.6 g. State the absolute error and the percentage error.
Solution: Absolute error = ±0.1 g. Percentage = 0.1 ÷ 125.6 × 100% = 0.08%.
Five students time a moto passing between two poles: 4.2 s, 4.5 s, 4.4 s, 4.3 s, 4.6 s. Give the result with its uncertainty and percentage error.
Solution: Mean = 22.0 ÷ 5 = 4.4 s. Uncertainty = (4.6 − 4.2) ÷ 2 = 0.2 s. Result: 4.4 s ± 0.2 s. Percentage = 0.2 ÷ 4.4 × 100% = 4.5%.
A length is 50.0 cm ± 0.5 cm. What is the percentage error?
Solution: 0.5 ÷ 50.0 × 100% = 1%.
Uwase measures the density of water as 0.96 g/cm³. The accepted value is 1.00 g/cm³. Find her percentage error.
Solution: 0.04 ÷ 1.00 × 100% = 4%.
Which is more precise: 12.0 s ± 0.1 s or 120 s ± 0.5 s?
Solution: 0.1 ÷ 12.0 = 0.83%, and 0.5 ÷ 120 = 0.42%. The 120 s ± 0.5 s timing is more precise, even though its absolute error is larger.
Summary
Sources and credits
The Rwandan examples, worked examples and practice items are written by Ganzaa.
