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The Real Number System

Q. N. Z. W. IR. The Real Number System. Presented by Mr. Laws 8 th Grade Math JCMS. Goal/Objective. 8.NS : Know that there are numbers that are not rational and approximate them by rational numbers .

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The Real Number System

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

  2. 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.

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

  4. 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)

  5. Real Numbers Definitions • Real Numbers – consists of all rationaland 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

  6. 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, …}

  7. 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, …}

  8. 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}

  9. 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…, ,

  10. 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 • http://www.joyofpi.com/pi.html .001, .0011, .00111, .001111…etc

  11. Real Numbers Rational Numbers Irrational Numbers Real Number System Tree Diagram Terminating Decimals Repeating Decimals Integers Non-Terminating And Non-Repeating Decimals Whole Numbers Negative #’s Natural #’s Zero

  12. 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.

  13. Your Turn Answer True or False to the statements below. If the statement is False, explain why. 6. −5 is a rational number. _______ 7. is rational. _______ 8. is a natural number __________ 9. is an integer. _______ 10. 2.434434443… is a rational number.____________

  14. 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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