1. Chapter 1: Real Numbers and Equations Section 1.1: The Set of Real Numbers

2. In this section we will review: The elements of the set of real numbers and represent them on a number line

3. Section 1.1: The Set of Real Numbers Real Numbers – Numbers that you use in everyday life Real numbers can be either rational or irrational Rational number – can be expressed as a ratio m/n, where m and n are integers and n is not zero. The decimal form is either terminating or repeating Ex. 1/6, 1.9, 2.575757…, -3, √4, 0

4. Section 1.1: The Set of Real Numbers Irrational number – number that is not rational Cannot be written as a ratio Decimal form neither terminates nor repeats Ex. √5, π, 0.01001000100001…

5. Section 1.1: The Set of Real Numbers Natural numbers – {1, 2, 3, 4, 5, …} Whole numbers - {0, 1, 2, 3, 4, …} Integers – {-3, -2, -1, 0, 1, 2, …} ALL are subsets of the rational numbers

6. The Real Number System Rational Numbers Irrational Numbers A non- repeating, non- ending decimal Integers Whole Numbers Natural Numbers {…, -3, -2, -1, 0, 1, 2, 3, …} {0, 1, 2, 3, …} {1, 2, 3, …} Any number that can be expressed as a fraction where the denominator is not a zero (the decimal either repeats or ends)

7. Section 1.1: The Set of Real Numbers Example 1 Name the sets of numbers to which each number belongs √25 -32 √18 -3/4 0.272727…

8. Section 1.1: The Set of Real Numbers Example 2 Show that the terminating decimal 0.225 is rational by writing it as the quotient of two integers

9. Section 1.1: The Set of Real Numbers Example 3 Show that the repeating decimal can be written as the quotient of two integers Let N = 0.272727… 100 N = 27.272727… 99 N = 27 N =

10. Section 1.1: The Set of Real Numbers Example 4 Show that the repeating decimal can be written as the quotient of two integers

11. Section 1.1: The Set of Real Numbers Example 5 Draw a number line and graph each of these real numbers. Label each point with its coordinate -3, 3.5, 5,, -4.5, -0.25

12. Section 1.1: The Set of Real Numbers Homework Practice Exercises: Pg. 5 #2-66 (even)