Classifying and Identifying Real Numbers as opposed to

Classifying and Identifying Real Numbers (as opposed to fake numbers? ) 1

Objective Identify and classify rational and irrational numbers 2

THINK SHARE How many numbers are between 0 and 1 on the number line? 3

Real Numbers are every number. Therefore, any number that you can find on the number line. Real Numbers have two categories.

Two Kinds of Real Numbers • Rational Numbers • Irrational Numbers 5

Rational Numbers • A rational number is a real number that can be written as a ratio (fraction) of two integers. • A rational number can be written as an integer, terminating or repeating decimal. 6

Examples of Rational Numbers • 16 • 1/2 • -8 • 1. 3333… • - 3/4

Integers One of the subsets of rational numbers

Integers • Consist of the natural numbers, their opposites and zero -4, -3, -2, -1, 0, 1, 2, 3, 4 9

Integers • Integers are rational numbers because they can be written as fraction with 1 as the denominator. 10

Types of Integers • Natural Numbers(N): Natural Numbers are counting numbers from 1, 2, 3, 4, 5, . . . . • Whole Numbers (W): Whole numbers are natural numbers (counting numbers and zero. 0, 1, 2, 3, 4, 5, . . . . 11

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Irrational Numbers • An irrational number is a number that cannot be written as a ratio (fraction) of integers. • In decimal form, they are the numbers that are non-terminating and non-repeating. 13

Examples of Irrational Numbers • Square roots of non-perfect “squares” 5 2. 2360 • Pi 3. 1415……

Try this! Thumbs up- rational Thumbs down- irrational • a) Irrational • b) Irrational • c) Rational • d) Rational • e) Irrational

Quick Question? ? ? 16

Classifying Real Numbers Write all classifications that apply to each number. I DO. 5 is a whole number that is not a perfect square. irrational, real WE Do. – 12. 75 is a terminating decimal. rational, real 5 16 16 4 = =2 You Do 2 2 2 whole, integer, rational, real

Exit Ticket State if each number is rational, irrational, or not a real number. A. 21 irrational B. 0 3 0 =0 3 rational

Steps for Comparing • One type of problem strategy is to use a visual. • Today’s visual is the number line. 19

Model • Change the numbers to a decimal. • Is the number greater than zero? • What two whole numbers is the number between? • Is it closer to a quarter? a half? three-quarters? 20

WE DO-Practice Rally Coach • Partner A asks the questions and Partner B responds by answering and placing the number on the number line. • Partner B asks the questions and Partner A responds by answering and placing the number on the number line. 21

I Do • Place the following numbers on the number line. 22

Thinking for Tomorrow • Where do you think the following numbers would fall on the number line? • √ 15 √ 9 23