Chapter 1. Review of Numerical Computation

OBJECTIVES When you have completed this chapter, you should be able to Perform basic arithmetic operations on signed numbers. Perform basic arithmetic operations on approximate numbers. Take powers, roots, and reciprocals of signed and approximate numbers. Perform combined arithmetic operations to obtain a numerical result. Convert numbers between decimal, scientific, and engineering notation. Perform basic arithmetic operations on numbers in scientific and engineering notation. Convert units of measurement. Substitute given values into formulas. Solve common percentage problems.

We start this first chapter with some definitions to refresh your memory of terms you probably already know. We will point out the difference between exact and approximate numbers, a distinction you may not have made in earlier mathematics classes. Then we will perform the ordinary arithmetic operations—addition and subtraction, multiplication and division—but here it may be a bit different from what you are used to. We will use the calculator extensively, which is probably not new to you, but now we will take great care to decide how many digits of the calculator display to keep. Why not keep them all? We will show that when working with approximate numbers keeping too many digits is misleading to anyone who must use the result of your calculation. As a further complication, we will combine both exact and approximate numbers, as well as positive and negative numbers, or signed numbers. As we proceed, we will point out some rules that will help get us ready for our next chapter on algebra, which is a generalization of arithmetic.