As is known, the result of an experiment is calculated by performing mathematical operation (like addition, subtraction, multiplication, division, etc.) on several measurements, which have different degrees of accuracy. It has been established that (a) When `x= a+b , Delta x = +- (Delta a + Delta b)` (b) When `x= a -b , Delta x = +- (Delta a + Deltab)` (c ) When `x = axxb , (Deltax)/(x) = +- ((Deltaa)/(a) +(Deltab)/(b))` (d) When `x = (a)/(b) , (Deltax)/(x) = +-((Deltaa)/(a) + (Deltab)/(b))` Read the above paragraph and answer the following questions : (i) Why is absolute error in `x = (a -b)`, sun of the absolute error in a and b ? (ii) Why is fractional error in `x=(a)/(b)` , sun of fractional error in a and b ? (iii) What do you learn from this ?

As is known, the result of an experiment is calculated by performing m

1.	As is known, the result of an experiment is calculated by performing mathematical operation (like addition, subtraction, multiplication, division, etc.) on several measurements, which have different degrees of accuracy. It has been established that (a) When `x= a+b , Delta x = +- (Delta a + Delta b)` (b) When `x= a -b , Delta x = +- (Delta a + Deltab)` (c ) When `x = axxb , (Deltax)/(x) = +- ((Deltaa)/(a) +(Deltab)/(b))` (d) When `x = (a)/(b) , (Deltax)/(x) = +-((Deltaa)/(a) + (Deltab)/(b))` Read the above paragraph and answer the following questions : (i) Why is absolute error in `x = (a -b)`, sun of the absolute error in a and b ? (ii) Why is fractional error in `x=(a)/(b)` , sun of fractional error in a and b ? (iii) What do you learn from this ?
Answer» (i) We have made error twice , in measuring a and in measuring b. Therefore, absoute error in x = (a -b ) has to be sum of the two errors. (ii) Same argument applies to fractional error in x = a//b. (iii) From this study, we learn that errors committed any number of times just add. No mathematical operation can reduce the net overall error. So be warned ! Multiple errors are going to cost you dearly.