If the true value of a quantity is 3.2 and the absolute error must be less than 0.05, find the acceptable measured values.

Question

If the true value is 3.2 and the absolute error must be less than 0.05, find the acceptable measured values.

a) 3.15<x<3.25 b) x<-3.15 0r x>3.25 c) x< 3.15 or x>3.15 d) -3.15<x<3.25

Answer 1

The absolute error shows by how much the experimental value differs from the true value. So experimental value may end up greater or smaller than the true value, therefore if the error is 0.05, it means that acceptable values are either smaller or greater than the true value by no more than 0.05. If true value is 3.2, then acceptable values are not smaller than 3.2-0.05=3.15 or not greater than 3.2+0.05=3.25. It can be written as follows:

3.15<x<3.25

 

Thus correct answer is a)

Answer 2

lower limit: 3.2 - .05 = 3.15

 

upper limit: 3.2 + .05 = 3.25

 

so, 3.15 < x < 3.25