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**Mrs.Volynskaya Real Numbers**

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**The Set of Natural Numbers: {1, 2, 3,…}**

The Set of Whole Numbers: {0, 1, 2, …} The Set of Integers {… -3, -2, -1,0,1,2…} Rational numbers can be written as fractions or as decimals that either terminate or repeat: 2/7, 0.354, , 4/5, Irrational numbers can only be written as decimals that do not terminate or repeat. If a whole number is not a perfect square, then its square root is an irrational number. √2, √3, √5 are Irrational How about √1, √4 , √9, √16 ???

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WORLD OF REAL NUMBERS

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EXAMPLE Classify all the following numbers as natural, whole, integer, rational, or irrational. List all that apply. 117 … -½ 6.36 1/9 -3

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**EXAMPLE -3 is an integer and a rational number.**

77 is a Natural number, a Whole number, an Integer, and a Rational number. 9/10 is a rational number. (- 5) is an integer, and a rational number. … is an irrational number. -3 is an integer and a rational number. 5.39 is a rational number. is an irrational number. 1/7 is a rational number.

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Set A collection of objects. Set Notation { } Natural numbers Counting numbers {1,2,3, …} Whole Numbers Natural numbers and 0. {0,1,2,3, …} Integers Positive and negative natural numbers and zero. {… -2, -1, 0, 1, 2, 3, …} Rational Number A real number that can be expressed as a ratio of integers (fraction) Irrational Number Any real number that is not rational. Real Numbers All numbers associated with the number line.

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**Copyright © 2011 Pearson Education, Inc.**

To which set(s) of numbers does 6 belong? a) Natural Numbers b) Whole numbers c) Integers d) Rational numbers e) Irrational numbers f) Real numbers Copyright © 2011 Pearson Education, Inc.

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**Copyright © 2011 Pearson Education, Inc.**

To which set of numbers does 6 belong? a) Natural Numbers b) Whole numbers c) Integers d) Rational numbers e) Irrational numbers f) Real numbers Copyright © 2011 Pearson Education, Inc.

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**Definitions A symbol that can vary in value. Variable**

A symbol that does not vary in value. Constant A mathematical relationship that does not contain an equal sign Expression A mathematical relationship that contains an equal sign. Equation A mathematical relationship that contains an inequality symbol (, <, >, , or ). Inequality Vocabulary Matching Cards Absolute Value A given number’s distance from 0 on a number line. Notation = | |.

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