The method of significant digits would have had us believe otherwise. It can get rather tricky to compute bounds via interval arithmetic. To compute the low bound in the last example, we had to use the smallest possible values for the measurements in the numerator and the largest possible values for the measurements in the denominator, and then reverse the process to obtain the high bound. We give it as its argument the expression that we wish to evaluate with the measurements enclosed in backquotes. If a computation involves a number that is NOT a measurement, we simply leave off the backquotes and write it as usual.
Exercises Doing interval arithmetic can take a big of ingenuity.
Given the ranges in which several the measurements involved in a calculation must lie, you must figure out what is the smallest possible answer and what is the largest possible answer. If you don't have access to Maple and our library functions, it can take a bit of thought. As a final exercise, we will give some expressions. Use interval arithmetic to calculate the interval in which the true value must lie, and compare it to the result predicted by the method of significant digits. As always, try out some examples of your own.