If your measurement of some quantity is uncertain and this measurement enters in
ID: 1424948 • Letter: I
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. Then, for all you know the edge could be as long as I lin or as short as 10in. 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 of carpet = l*l = (10.5 in)2 = 110.25 in2
Error in measuring area = 2 * delta_l / l = 2 * (5/100 * 10.5 ) / 10.5 ( delta _l = 5 * 10.5 /100)
= 1.05
min area of Carpet = 110.25 - 1.05 = 109.2 in2
Max area of carpet = 110.25 + 1.05 = 111.3 in2