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

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2 Objective Identify and classify rational and irrational numbers 2

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

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

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5 Two Kinds of Real Numbers Rational Numbers Irrational Numbers

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6 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.

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Examples of Rational Numbers 16 1/2 -8 1.3333… - 3/4

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Integers One of the subsets of rational numbers

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

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

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11 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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13 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.

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Examples of Irrational Numbers Square roots of non-perfect “squares” Pi 3.1415…… 5 2.2360

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

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Quick Question??? 16

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Classifying Real Numbers Write all classifications that apply to each number. 5 is a whole number that is not a perfect square. 5 irrational, real –12.75 is a terminating decimal. –12.75 rational, real 16 2 whole, integer, rational, real = = 2 4242 16 2 I DO. WE Do. You Do

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State if each number is rational, irrational, or not a real number. 21 irrational 0303 rational 0303 = 0 Exit Ticket A. B.

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

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20 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

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21 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

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

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23 Thinking for Tomorrow Where do you think the following numbers would fall on the number line? √15 √5 √9 23

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