Real Numbers and The Number Line

Objectives Classify numbers and graph them on number lines. Tell which of two real numbers is less than the other. Find the additive inverse of a real number. Find the absolute value of a real number.

Square Root

A square root is one of two equal factors of a number. For example one square root of 64 is 8 since 64 is 8or 88 2

A number like 64, whose square root is a rational number is called a perfect square

25 is 5or 55 236 is 6or 66 2

Example

Square RootThe symbol called a radical sign, is used to indicate the principal square root of the expression under the radical sign

864 For example

64 ofroot square principal theindicates

864 64 ofroot square negative theindicates

864 64 of roots squareboth indicates

Note that is not the same as .

64 64 is not a real number since no real number multiplied by itself is negative

64

Find Square Roots

121 d.

0144.0 c.

81.0 b.

9

16 a.

3

4

b

a

b

a :note

9.0

12.0

numbers realfor undefined is 121

NATURAL NUMBERS {1, 2, 3,…}

WHOLE NUMBERS {0, 1, 2, 3,…}INTEGERS {…-2, -1, 0, 1, 2,…}

RATIONAL NUMBERS

Any number that can be written in fraction form is a rational number. This includes integers, terminating decimals, and repeating decimals.

Irrational numbersNumbers that can not be expressed as rational numbers.

Objective 1 Classify numbers and graph them on number lines

Real Numbers

Rational Numbers

Irrational Numbers

2 31 ...4

Natural Numbers

Whole Numbers

0

Integers 1

23

...4

1

2

4

3

25.0

33.02

...14159.3

...73205.13

5

The set of Real Numbers consists of the set of rational numbers and the set of irrational numbers.

Examples of Rational numbers

51

5

- 71

7

01

0

5

2fraction

aalready

0.310

3

3.03

1

...714285714285.07

3375.08

3

EXAMPLES OF IRRATIONAL NUMBERS

....89897948.424 .....73205080.13

....141592654.3 ....718281824.2e

the is a whole number, but the , since It lies between 5 and 6,must be irrational.

36 30

36 25

..5.4772255. 30

Answer: irrational and real

Name the sets of numbers to which belongs.

lies between 2 and 3 so it is not a whole number.

Answer: natural , whole , integer , rational, and real

Name the sets of numbers to which belongs.

Name the sets of numbers to which each number belongs.

a.

b.

c.

d.

Answer: rational and real

Answer: rational and real

Answer: irrational and real

Answer: natural , whole , integer rational and real (R)

 

Answer: rational and real

Answer: natural , whole , integer rational and real (R)

Answer: irrational and real

Answer: integer rational and real (R)

 

 

 

 

Example: Graph: ( -4, -2, 0, ,4, )

2

5 48

93.6

Each point on the number line corresponds to exactly one real number

Completeness Property

Replace the with <, >, or = to make the sentence true.

Since the numbers are equal.

Answer:

19614

Objective 2 Tell which of two real numbers is less than the other

Replace the with <, >, or = to make the

sentence true.

Answer:

9.648

Objective 2 Tell which of two real numbers is less than the other

greatest least to fromorder in 20

53,

3

8,7 ,63.2 Write

65.220

53

2.667 .....666666.23

8

646.2....64575131.27

2.636 ....636363.263.2

decimal a asnumber each Write

667.2636.2646.265.2

Objective 2 Order Real numbers from least to greatest

greatest least to fromorder in 1.5- and,2,3

2,4.0 ,4 Write

1.5- 41.12 0.67- 0.4 24

decimal a asnumber each e Writ

241.14.067.05.1

From the least to the greatest

Order Real numbers from least to greatest

The opposite of 5 is 5The opposite of -3 is 3

When you add two opposite numbers , the sum is always 0.

0)2(2

0)( aa

044

Objective 3 Find the additive inverse of a real number.

The opposite of 5 is 5

The absolute value of any number n is its distance from zero on a number line and is represented as n

Example:

33 and 33

01 1 2234 3 4 5

3 units 3 units

Objective 4 Find the absolute value of a real number

END OF LESSON