As we have seen in the first two part of this series it is easier to determine the uncertainty when addition and subtraction is involved but also to determine uncertainty when multiplication and division is involved.
Today we are going to see how to determine the uncertainty when a power is involved.
Very often a derived quantity is determined basic or othere derived quantities using powers, roots, etc.
As we are going to see the method to determine the uncertainty in these three cases are similar and can be adapted to other derived quantities.
Let us have a look at how to determine the uncertainty in volume.
A cube has length of L = 20.4+_0.2cm
Determine the uncertainty in volume.
V = L3
V = L*L*L
=249 = 200 (1 sf because of 0.2 )
V = L3
=8500 (2 sf because of 200)
Hence V = 8500+_200 cm3
After you have studied this example are you able to know how to find the uncertainty in any other derived quantities?
Then can you deduce the fractional uncertainty?
Where K is a dimensionless constant with no uncertainty.
When there is a dimensionless constant with no uncertainty it does not enter in the equation to calculate the fractional uncertainty.
The area of a circle is given by the equation
If the radius r =10.1+_0.5 cm
then calculate the fractional uncertainty and the uncertainty in A.