OPERATIONS ON APPROXIMATE QUANTITIES

It is important to know how to estimate the accuracy of the result produced. There are many sources of error. This chapter discusses the sources of errors in results of computation and operations on approximate quantities. The initial data for the calculation are often obtained from experiments and any experiment can produce results of only limited accuracy. In rounding, one substitute an approximate number for the number in question. The error arising here is called the rounding error. The computations produce not an exact value but a certain region in which the exact value is situated, even if all the rest of the calculations are performed exactly without rounding. This is referred as an indeterminate region. The boundaries of this region determine the limits of error independently of the method of writing the numbers. This error is called an irremovable error.