Question

Imagine you measure the length of 15 cars, and then sum that length, in order to see how big a parking lot must be. You do this in two different ways. First, you use the same bad tape measure for each car so that your measurement is always 1 cm too long, or always too short, for all of the measurements. For your second attempt, you use a different bad tape measure for each car, so there is an uncertainty of plus or minus 1cm in each measurement. What is your estimate of the total error in the sum of all the car lengths in these two cases

Answer 1

± 15 cm

Explanation:

In the first case, since the measurement is 1 cm too long or too short, the error is ± 1 cm.

In the second case, the uncertainty or error is also ± 1 cm.

Now, since there are 15 cars, and there is an error of ± 1 cm in each measurement, by the error formula the total error in the sum of both cases is 15 × ±1 cm = ± 15 cm

So, the total error in both cases is ± 15 cm.