Asked by Omar
Helen draws a random circle. she then measure it diameter and circumference. should get a circumference, C, of 405mm correct to 3 significant figures she get a diameter, D, of 130mm correct 2 significant figures. Helen want to find the value of Pi using a formula Pi =D/C calculate the lower bound and upper bound for Helen's value of pi give your answer correct to 3 decimal place?
First, you want to find the lower and upper bounds of the circumference C and diameter D.
C = 405mm to 3sf so the bounds are:
404.5 to 405.5
We find this by subtracting/adding half the degree of accuracy. Here it is 1mm, looking at 3rd significant figure.
D = 130mm to 2sf so the bounds are:
125 to 135
Here the degree of accuracy is 10mm, looking at the 2nd significant figure.
Now you conside... more
If we’re looking for the lowerbound of pi, the circumference C would have to be at its smallest and the diameter D would have to be at its highest. For the upper bound it would be the other way around.
So for the lower bound:
405mm (3 s.f.) => 404.5 (lowest possible)
130mm (2 s.f.) => 134.499... (highest possible)
lower bound pi = 3.007 (3d.p)
So for the higher bound:
405mm (3 s.f.) => 405.49... more