If your measurement of some quantity is uncertain and this measurement enters in

Question

If your measurement of some quantity is uncertain and this measurement enters into some formula then the results of that formula will also be in uncertain. This effect is often called the propagation of error and is illustrated by the following question. 8. Suppose you measure a square piece of carpet to have an edge of length 10.5 in. Assume that your measurement has a 5% uncertainty. Thsn, for all you know the edge could be as long as 11 in or as short as lOin. In light of this what are the maximum and minimum values for the carpet's area. What is the percent uncertainty in the carpet's area and how does this relate to the percentage uncertainty of its edge?

Explanation / Answer

area = L^2 = (10.5*10.5)

area = 110.25

percent uncertainity = (5% + 5%)

obsolute uncertainity = 0.1*110.25 = 11.025 in^2

area = 110.25 +/- 11.025

maximum area = 110.25 + 11.025 = 121 in^2

minimum area = 110.25-11.025 = 99 in^2

area = 110.25 +/- 11.025

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