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**Presented by Mr. Laws 8th Grade Math JCMS**

The Real Number System Presented by Mr. Laws 8th Grade Math JCMS N W Z Q IR

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Goal/Objective 8.NS: Know that there are numbers that are not rational and approximate them by rational numbers. 8.NS.1: Understand informally that every number has a decimal expansion; the rational numbers are those with decimal expansions that terminate in zeros or eventually repeat. Know that other numbers are called irrational numbers.

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Essential Question How do I understand and perform operations with the Real Number System? Q N Z W IR

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The Real Number System The Real Number System is made up of a set of rational and irrational numbers. It has at five subsets: Rational Numbers (Q) Integers (Z) Whole Numbers (W) Natural Numbers (N) Irrational Numbers (IR)

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**Real Numbers Definitions**

Real Numbers – consists of all rational and irrational numbers. It includes any number that can be written as a fraction, mixed numbers, terminating and repeating decimals, whole numbers, integers. O -6 4

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Rational Numbers Rational Numbers – consists of integers, terminating, and repeating decimals. It can also be expressed as a fraction. {…-3, -2, -1, 0, 1, 2, 3, …}

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Rational Numbers Integers – consist of natural numbers, their opposites (negative #’s), and zero. It does not include fractions or decimals. All whole numbers are integers. For example: {…-3, -2, -1, 0, 1, 2, 3, …}

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Integers Whole numbers – consist of natural numbers and zero. {0, 1, 2, 3, 4,…} Natural numbers – are all the counting numbers. {1, 2, 3, 4…} Negative numbers ={…-4, -3, -2, -1}

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Rational Numbers Terminating Decimals are rational numbers that stops before or after the decimal point. For example: 5.0, 2.75, .40, .0001…etc. Repeating Decimals are rational numbers that repeats after the decimal point. For example: .3333…, ,

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Irrational Numbers Irrational numbers consist of numbers that are non-terminating and non-repeating decimals. They cannot be express as a fraction! Pi is an great example of an irrational number .001, .0011, , …etc

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**Real Number System Tree Diagram**

Rational Numbers Irrational Numbers Terminating Decimals Repeating Decimals Integers Non-Terminating And Non-Repeating Decimals Whole Numbers Negative #’s Natural #’s Zero

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**Your Turn 1. How are the natural and whole numbers different?**

2. How are the integers and rational numbers different? 3. How are the integers and rational numbers the same? 4. How are integers and whole numbers the same? 5. Can a number be both rational and irrational? Use the diagram to explain your answer.

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Your Turn Answer True or False to the statements below. If the statement is False, explain why. 6. −5 is a rational number. _______ is rational. _______ is a natural number __________ is an integer. _______ … is a rational number.____________

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**Summary What did you learn in this lesson?**

What are some important facts to remember about the real number system? Is there something within the lesson that you need help on?

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