If the mass of a block is measured as
and the volume as
then 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 quantity
is
then 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 then
so the density is
Power relationships are a special case of this. If
then
If a cube is measured to be
along each side then the % uncertainty in the volume is
and the absolute uncertainty is 7.5% of
so the volume is
If two quantities are added, then the absolute uncertainty in the sum is the sum of the absolute uncertainties, so if
and
then
Sometimes however we can only estimate the range of a quantity. If
then 
is between 55 and 65 degrees.
is between
and
The uncertainty is the maximum value of
and
i.e. 0.5 so
to 2 dp.