Sets of Numbers

Students will be able to distinguish between different

sets of numbers.

Algebra Review 2FHS

Numbers and Variables

• 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.

In mathematics, vocabulary words are very important. We need to be precise so we all know what we are talking about.

Algebra Review 3FHS

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.

Algebra Review 4FHS

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.

ab

Some examples of irrational numbers are: and 2

Algebra Review 5FHS

How are these Numbers Related?• Here is a diagram of how these numbers are

related.

Natural Numbers (N)

Real Numbers (R)

Irrational NumbersWhole Numbers (W)

Integers (Z)

Rational Numbers (Q)

Algebra Review 6FHS

Classify the Numbers• -2.5

• 5

•

• 0.121221222. . .

•

5

Rational number, Real number

Natural number, Whole number, Integer, Rational number, Real number

Irrational number, Real number

Irrational number, Real number

Rational number, Real number0.123

Algebra Review 7FHS

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.

Algebra Review 8FHS

Graphing Numbers • Graph each of these numbers on the

same number line:

2.53

14

2.56 1

| | | | | | | |

-3 -2 -1 0 1 2 3 4

Algebra Review 9FHS

Ordering Real Numbers• Put these numbers in order from smallest to

largest number: 73

93

34

3.56 3.7211

• First, change all the numbers to their decimal equivalents:

7

3 3.79

3

3 3.754

3.56

3.72 3.14

11 3.32

• Then put the numbers in order:

73

93

34

3.56 3.72 11

Algebra Review 10FHS

Ordering Real Numbers• What is different if the numbers are

negative?

• Put these numbers in order from smallest to largest number:

7

39

3.72 • First, change all the numbers to their

decimal equivalents:

7

3 3.79

3.72 3.14

• Then put the numbers in order:

73

9 3.72