Chapter 8.2, Problem 23P

The following problem illustrates a danger that occurs because of round-off error when nearly equal numbers are subtracted and the difference is then multiplied by a largenumber. Evaluate the quantity

$1000.\left|\begin{array}{cc}6.010& 18.04\\ 2.004& 6.000\end{array}\right|$

in the following ways:

a) First round each entry in the determinant to two digits.

b) First round each entry in the determinant to three digits.

c) Retain all four digits. Compare this value with the resultsin parts (a) and (b).