Sets of Numbers Students will be able to distinguish between different sets of numbers.

Numbers and Variables In mathematics, vocabulary words are very important. We need to be precise so we all know what we are talking about. There are several different sets of numbers that we will be exploring: These are natural numbers, whole numbers, integers, rational numbers, irrational numbers and real numbers. FHS Algebra Review

Types of Numbers The natural numbers (sometimes called counting numbers) consists of the numbers {1, 2, 3, . . .} The whole numbers consists of the set of natural numbers plus 0, or {0, 1, 2, 3, . . . } The set of integers consists of the whole numbers and their opposites, or { . . . , -2, -1, 0 1, 2, 3, . . . } There are other numbers on the number line as well as the integers. Numbers such as: ½, 3.8, ¾, -1.9 can also be represented on the number line. FHS Algebra Review

Types of Numbers (cont.) Any number that can be written as the quotient of two integers , where a and b are integers and b is not 0) is a rational number. An irrational number is one that can’t be written this way. Together the set of rational and the set of irrational numbers make up the set of real numbers. Some examples of irrational numbers are: and FHS Algebra Review

How are these Numbers Related? Here is a diagram of how these numbers are related. Real Numbers (R) Rational Numbers (Q) Integers (Z) Irrational Numbers Whole Numbers (W) Natural Numbers (N) FHS Algebra Review

Classify the Numbers -2.5 5 0.121221222. . . Rational number, Real number Natural number, Whole number, Integer, Rational number, Real number Irrational number, Real number Irrational number, Real number FHS Algebra Review

Graphing Numbers All real numbers can be graphed on a number line. The number that corresponds to a point on a number line is called the coordinate of the point. Each real number corresponds to exactly one point on a number line. The point that corresponds to the number is called the graph of the number, and is indicated by a solid dot. FHS Algebra Review

Graphing Numbers Graph each of these numbers on the same number line: | | | | | | | | -3 -2 -1 0 1 2 3 4 FHS Algebra Review

Ordering Real Numbers Put these numbers in order from smallest to largest number: First, change all the numbers to their decimal equivalents: Then put the numbers in order: FHS Algebra Review

Ordering Real Numbers What is different if the numbers are negative? Put these numbers in order from smallest to largest number: First, change all the numbers to their decimal equivalents: Then put the numbers in order: FHS Algebra Review