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

Chapter 1: Real Numbers and

EquationsSection 1.1: The Set of Real Numbers

Section 1.1: The Set of Real Numbers

• In this section we will review: • The elements of the set of real numbers and

represent them on a number line


• 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


• Irrational number – number that is not rational• Cannot be written as a ratio• Decimal form neither terminates nor

repeats• Ex. √5, π, 0.01001000100001…


• 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

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)

6 ,5 ,3

,2 , :Ex


• Example 1• Name the sets of numbers to which each number

belongs• √25

• -32

• √18

• -3/4

• 0.272727…


• Example 2• Show that the terminating decimal 0.225 is

rational by writing it as the quotient of two integers


• 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 =


• Example 4• Show that the repeating decimal can

be written as the quotient of two integers


• 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


• Homework• Practice Exercises: Pg. 5 #2-66 (even)

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