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**Lesson 9.2 The Real Number System**

Objective - To classify and identify numbers within the real number system.

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**Understanding Rational and Irrational**

“Makes Sense” “Doesn’t Make Sense” Rational Numbers Irrational Numbers -Any number that can be written as a fraction. -Non-terminating and non-repeating decimals. fractions -can’t be written as a fraction. wholes integers terminating decimals repeating decimals

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**Sets of Numbers Naturals - Natural counting numbers. { 1, 2, 3… }**

{ 1, 2, 3… } Wholes - Natural counting numbers and zero. { 0, 1, 2, 3… } Integers - Positive or negative natural numbers or zero. { … -3, -2, -1, 0, 1, 2, 3… } Rationals - Any number which can be written as a fraction. Irrationals - Any decimal number which can’t be written as a fraction. A non-terminating and non-repeating decimal. Reals - Rationals and irrationals.

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**…-3, -2, -1, 0, 1, 2, 3... …-3, -2, -1 Sets of Numbers Reals Rationals**

Irrationals - any number that can be written as a fraction. - non-terminating and non-repeating decimals , 7, -0.4 Fractions/Decimals Integers , -0.32, - 2.1 …-3, -2, -1, 0, 1, 2, 3... Negative Integers Wholes …-3, -2, -1 0, 1, 2, 3... Zero Naturals 1, 2, 3...

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Sets of Numbers This is a Venn Diagram that displays the following sets of numbers: Naturals, Wholes, Integers, Rationals, Irrationals, and Reals. Reals Rationals -2.65 Integers -3 -19 Wholes Irrationals Naturals 1, 2, 3...

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**Identify each number below as natural, whole,**

integer, rational, irrational, or real. More than one may apply. Rational , Real Whole , Integer , Rational , Real Integer , Rational , Real Irrational , Real Natural ,Whole , Integer , Rational , Real

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**Identify each number below as natural, whole,**

integer, rational, irrational, or real. More than one may apply. Rational , Real Integer , Rational , Real Natural ,Whole , Integer , Rational , Real Integer , Rational , Real Irrational , Real

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**Graph on Number Line (Hint: turn them all into decimals) -1 1 2 3 4 5**

1 2 3 4 5 6

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**Order From Least to Greatest**

-3 -4 -2 -1 1 2 4 5 6 7 3

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**Compare Using < > or =**

Turn them both either to: Fractions and use the heart method Decimals and compare place values

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**Use <, >, or = to compare.**

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**Homework Page 455 (12-46) even Write the title**

Write the number and question Show work Highlight answer

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