Uncertainties in Calculations
If the mass of a block is measured asand the volume asthen we can work out the density:
The largest possible value of the density is
The smallest possible value of the density is
We can round these to give
If the uncertainty in a quantityisthen the fractional uncertainty is and the percentage uncertainty is
The % uncertainty in the density above is
Rules for Multiplication, Division or Powers of Uncertain Values
When two or more quantities are multiplied or divided we take the resulting % error as the sum of the %percentage uncertainties.
For the example above,and
The total % uncertainty in the density is thenso the density is
Power relationships are a special case of this. IfthenIf a cube is measured to bealong each side then the % uncertainty in the volume isand the absolute uncertainty is 7.5% ofso the volume is
If two quantities are added, then the absolute uncertainty in the sum is the sum of the absolute uncertainties, so ifandthen
Sometimes however we can only estimate the range of a quantity. Ifthen is between 55 and 65 degrees.is betweenandThe uncertainty is the maximum value ofandi.e. 0.5 soto 2 dp.