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Example from Physics, 1.3 The Language of Physics: Physical Quantities and Units
A series of shingles are used to protect the roof of a home. Using a measuring tape, you measure one shingle and find its dimensions to be 44 cm by 100 cm. Knowing that your measurements are not perfect, you estimate an uncertainty of ±0.5 cm. Following the method of adding percents, what is the area of the shingle, including uncertainty?
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
While calculating the area of the shingle is straightforward (44 cm x 100 cm = 4400 cm2), determining the percent uncertainty is more challenging. In order to use the method of adding percents, you must first calculate the percent uncertainty of each measurement.
Length % Uncertainty: 𝜹A/A x 100% = 0.5/44 x 100% = 1.1%
Width % Uncertainty: 𝜹A/A x 100% = 0.5/100 x 100% = 0.5%
Adding Percents: 1.1% + 0.5% = 1.6% uncertainty
Area of the Shingle: 4400 cm2 ± 1.6%
Note that this uncertainty can also be expressed in metric terms.
1.6% x 4400 cm2 = 70.4 cm2
Area of the Shingle: 4400 ± 70.4 cm2
How did it go?