Question
A good-quality measuring tape can be off by 0.50 cm over a distance of 20 m. What is its percent uncertainty?
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Solution video
OpenStax College Physics for AP® Courses, Chapter 1, Problem 12 (Problems & Exercises)
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This is College Physics Answers with Shaun Dychko. A good 20 meter tape measure might have an error of 0.50 centimeters and so the question is what percentage is this error of a 20 meter measurement, the percent uncertainty in other words, and equation number 8 from chapter 1 tells us that; it's the absolute uncertainty—that's the name for this portion here this is the amount of error in a measurement— divided by the measurement itself times a hundred percent so when measuring 20 meters, you expect an error of about half of a centimeter. And so when we do this calculation, we need to make sure the units on the top and bottom are the same so this centimeters has to be converted into meters by multiplying by 1 meter for every 100 centimeters and the centimeters cancel leaving us with meters and then this works out to 0.025 percent. Now we do have two significant figures in our percent uncertainty; you never have more than that because it is an uncertainty after all and you can't really be very precise about your uncertainty so either one or two significant figures is appropriate.