Chapter: Mapping Math: Numbers
Introduction
This is the first chapter in the "Just Math" section of the Mapping Math book. This chapter is all about the different types of numbers. Numbers are the building blocks of mathematics, so it is important to understand the different types of numbers. Numbers can be organized into types according to some of there common characteristics. Some mathematical operations can only be performed with certain types of numbers, but not with other types of numbers. For example: You can take the square root of a negative number (unless you want to deal with imaginary numbers, a special type of number invented for just this purpose).
There is another important reason to learn about the different types of numbers. Computer programming languages typically work with different numbers in different ways, even representing different types of numbers in special ways. If you want to work with math in computer programming you'll need to understand these differences in the your particular programming language. Understanding the different types of numbers will help with this.
We will discuss the following types of numbers in this chapter:
- whole numbers (integers)
- even and odd numbers
- fractions
- numbers with a fractional part (real numbers)
- positive and negative numbers
- rational and irrational numbers
- really weird numbers
Remember that numbers can belong to more than one category. For example: The number -12 is a whole number and a negative number.
Online References
Counting Systems
Before we get into our discussion of the different types of numbers, it is important to briefly mention counting systems (otherwise known as number systems, numeral systems, or systems of numeration). Most of us have grown up using a base 10, or decimal number system. To put it simply, in a base 10 counting system you start to reuse digits to represent numbers after you have used the first 10 digits, 0 trough 9. (The eleventh digit in a base 10 number system is 10, which reuses the digits 1 and zero to represent the number ten.)
We use the base 10 (or decimal) counting system so much that we often forget that other counting systems are in use. For example: The base 2 (or binary) counting system, and the base 16 (or hexadecimal) system are very important in computer programming. Just remember when reading this chapter that we are dealing with the base 10 number system. A lot of the rules and facts we discuss won't apply to other counting systems. That's OK, because most land surveyors, cartographers, and other map makers or maps users will be working with the base 10 number system.
Online References
Decimal Number System Wikipedia Entry
Binary Number System Wikipedia Entry
Hexadecimal Number System Wikipedia Entry
Whole Numbers
The first type of number will look at are whole numbers. Whole numbers are also known as Integers. An integer is a number that has no fractional part. For Example: 4, -233, and 76 are all integers. The numbers 4.3, -233.568 and 76.001 are not integers. Whole numbers have some special qualities. They are typically easier to represent and manipulate in digital format. (Most computers really do work with whole numbers at the lowest level. If you think about it, a computer can represent the number 76.001 with 5 whole numbers and a decimal point.) Whole numbers are also all rational numbers, which we will talk about in a later section of this chapter. This means that it is easy to represent whole numbers in a base 10 number system that map makers typically use.