1. 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.

2. Square Root
A square root is one of two equal factors of a number.
For example one square root of 64 is 8 since
A number like 64, whose square root is a rational number is called a perfect square
Example

3. Square Root
The symbol called a radical sign, is used to indicate the principal square root of the expression under the radical sign
For example
Note that is not the same as
is not a real number since no real number multiplied by itself is negative

4. Find Square Roots

5. Numbers that can not be expressed as rational numbers.
Objective 1 Classify numbers and graph them on number lines
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 numbers
Numbers that can not be expressed as rational numbers.

6. Real Numbers
Rational Numbers
Integers
Irrational Numbers
Whole Numbers
Natural Numbers
The set of Real Numbers consists of the set of rational numbers and the set of irrational numbers.

7. Examples of Rational numbers5
- 7
0.3

8. EXAMPLES OF IRRATIONAL NUMBERS
the is a whole number, but the , since It lies between 5 and 6,must be irrational.

9. Name the sets of numbers to which belongs.
lies between 2 and 3 so it is not a whole number.
Answer: irrational and real
Name the sets of numbers to which belongs.
Answer: natural , whole , integer , rational, and real
Example 2-1c

10. a. b. c. d. Name the sets of numbers to which each number belongs.
Answer: rational and real
Answer: rational and real
Answer: irrational and real
Answer: natural , whole , integer rational and real (R)
Example 2-1f

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

12. Completeness Property
Each point on the number line corresponds to exactly one real number
Example: Graph: ( -4, -2, 0, ,4, )

13. Objective 2 Tell which of two real numbers is less than the other
Replace the with <, >, or = to make the sentence true.
Since the numbers are equal.
Answer:
Example 7-4a

14. Objective 2 Tell which of two real numbers is less than the other
Replace the with <, >, or = to make the sentence true.
Answer:
Example 7-4b

15. Objective 2 Order Real numbers from least to greatest

16. Order Real numbers from least to greatest
From the least to the greatest

17. Objective 3 Find the additive inverse of a real number.
The opposite of 5 is
The opposite of 5 is
The opposite of -3 is
When you add two opposite numbers , the sum is always 0.

18. Objective 4 Find the absolute value of a real number
The absolute value of any number n is its distance from zero on a number line and is represented as
Example:
and
3 units
3 units

19. END OF LESSON