Question
What is the height in meters of a person who is 6 ft 1.0 in. tall? (Assume that 1 meter equals 39.37 in.)
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Solution video
OpenStax College Physics for AP® Courses, Chapter 1, Problem 6 (Problems & Exercises)
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This is College Physics Answers with Shaun Dychko. The height of a person is 6 foot 1 and we want to convert this height into meters. Now when you see 6 feet and then followed by some number of inches, this is 6 feet plus that many inches so it's this many inches more than this many feet. And we can express the feet in terms of inches in order to get a total just number of inches because the conversion factor we are given is that there's 1 meter for every 39.37 inches. And so we multiply the 6 feet by 12 inches per foot and the feet cancel leaving us with inches here. So this works out to 72 inches plus this extra inch here for a total of 73.0 inches. Now this becomes the number 72 after you multiply 6 by 12 and you might be a bit confused about the significant figures here because if you add 72 to 1.0, strictly speaking, the answer should be 73 without the point 0 so just 73—no tenths place. However, in this particular calculation, we'll keep the point 0 and so we'll have this precision all the way to the tenths place because these are not two different measurements being added together— this is one single measurement— it's a single measurement 6 foot 1 and so this number here does not have any uncertainty in this digit at all because this number is part of the same measurement that created this one inch part as well. Now this is just a peculiarity of the way the imperial unit system expresses distances or heights so it expresses it as a sum of two different parts; some number of feet plus some number of inches. So yeah, this number here is not a separate measurement; if it was, if this was measuring something to be 72 inches and then you add that to 1.0 inches, the result would indeed be 73 with no decimal point here however, being all part of one single measurement, this is 73.0 inches, I like it. So that gets multiplied by our conversion factor, the inches cancel leaving us with meters and so we go 73 divided by 39.37 and we get 1.85 meters.