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Calculating Percent Uncertainty: A Bag of Apples · Physics Playground

Exercises Units and measurement

Example from Physics, 1.3 The Language of Physics: Physical Quantities and Units

Calculating Percent Uncertainty: A Bag of Apples

A grocery store sells 5-lb bags of apples. You purchase four bags over the course of a month and weigh the apples each time. You obtain the following measurements:

Week 1 weight: $4.8 lb$
Week 2 weight: $5.3 lb$
Week 3 weight: $4.9 lb$
Week 4 weight: $5.4 lb$

You determine that the expected weight of a 5 lb bag has an uncertainty of ±0.4 lb. What is the percent uncertainty of the bag’s weight?

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.

Strategy
First, observe that the expected value of the bag’s weight, $A$ , is 5 lb. The uncertainty in this value, $δ A$ , is 0.4 lb. We can use the following equation to determine the percent uncertainty of the weight

$% uncertainty = \frac{δ A}{A} × 100% .$
Solution
Plug the known values into the equation

$% uncertainty = \frac{0.4 lb}{5 lb} \times 100 % = 8 % .$

0 of 2 steps open

How did it go?

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From Physics (1st edition) by OpenStax (Rice University), section 1.3, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.

Strategy

Solution