Suppose that you measure two quantities, **x +/- dx** cm
and **y +/- dy** cm.
What happens to their uncertainties if you need to combine these values?

- If you add the quantities, their uncertainties just add.
total length = (x + y) cm uncertainty in total length = (dx + dy) cm

- If you subtract the quantities, again, their uncertainties ADD
(not subtract).
difference in length = (x - y) cm uncertainty in difference = (dx + dy) cm

- If you multiply the quantities, you must add their
**fractional**(or**percentage**) uncertainties to find the fractional (or percentage) uncertainty in the product.area of rectangle = (x * y) square cm uncertainty in area dx dy ------------------- = ( -- + -- ) (pure fraction) area x y dx dy uncertainty in area = ( -- + -- ) * ( area ) square cm x y

- If you divide the quantities, you must again add their
**fractional**(or**percentage**) uncertainties to find the fractional (or percentage) uncertainty in the ratio.x ratio of length to width = --- (pure fraction) y uncertainty in ratio dx dy ------------------- = ( -- + -- ) (pure fraction) ratio x y dx dy uncertainty in ratio = ( -- + -- ) * ( ratio ) (pure fraction) x y

- If you raise a value to a power
**N**, you multiply its fractional (or percentage) uncertainty by**N**to find the fractional (or percentage) uncertainty in the result.3 3 length cubed = x cm uncertainty in length cubed ( dx ) ---------------------------- = (----) * 3 (pure fraction) length cubed ( x ) dx 3 uncertainty in length cubed = (----) * 3 * (length cubed) cm x