If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation z =x/y. If the errors in x, y and z are Deltax, Deltay " and " Deltaz, respectively, then zpm Delta z= (x + y)/( y pm Delta y) = x/y (1 pm (Delta x )/( x ) ) ( 1 pm ( Delta y)/(y) )^(-1) The series expansion for(1 pm (Delta y )/( y) )^(-1) , to first power in Delta y // y " is " 1 pm (Delta y // y ).The relative errors in indepen- dent variables are always added. So the error in z will beDelta z = z ( (Delta x )/( x) + (Delta y )/( y) ) The above derivation makes the assumption that Delta x // x lt lt 1, Delta y // y lt lt 1 . The above derivation makes the assumption that Consider the ratior = (1 -a )/( 1 + a)to be determined by measuring a dimensionless quantity a. If the error in the measurement ofa isDelta a ( Delta a // a lt lt 1), then what is the error r in determining r ?