Question

Is it possible to increase the degree of accuracy by mathematical manipulations? Support your answer by an example.

Answer 1

It is not possible to increase the degree of accuracy by mathematical manipulations.
For example: When a number of values are added or subtracted, the result cannot be more accurate than the least accurate value.
If we add:      5.283
                 + 72.5
                      2.0014
We get        79.78314

In the above addition, 72.5 has the least accuracy. When we say 72.5, it implies that value lies between 72.45 and 72.55 and 72.5 is the most probable value. Thus the error in 72.5 is + 0.05. As the final result cannot be more accurate than the least accurate observation, so the correct and most reliable answer in the above addition is 72.9.