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1.8 The Real Number System

1.8 The Real Number System. Standard: 7.NS1d, 2c, & 2d. Goals & Objectives. To understand the real number system and recognize differences between rational and irrational numbers. To convert between different representations of rational and irrational numbers. Activites:.

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1.8 The Real Number System

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  1. 1.8 The Real Number System Standard: 7.NS1d, 2c, & 2d

  2. Goals & Objectives • To understand the real number system and recognize differences between rational and irrational numbers. • To convert between different representations of rational and irrational numbers.

  3. Activites: • Power Point notes and examples • Small Group Card Sort • Exit Ticket • Homework – Is it Rational?

  4. Real Numbers • Real numbers consist of all the rational and irrational numbers. • The rational numbers have many subsets: • Natural Numbers • Whole Numbers • Integers

  5. Natural Numbers • Natural numbersare the set of counting numbers. {1, 2, 3,…}

  6. Whole Numbers • Whole numbersare the set of numbers that include 0 plus the set of natural numbers. {0, 1, 2, 3, 4, 5,…}

  7. Integers • Integers are the set of whole numbers and their opposites. {…,-3, -2, -1, 0, 1, 2, 3,…}

  8. Rational Numbers • Rational numbers are any numbers that can be expressed as a ratio (in the form of ,where a and b are integers, and b ≠ 0). • They can always be expressed by using terminating decimals or repeating decimals.

  9. Terminating Decimals • Terminating decimals are decimals that contain a finite number of digits. • Examples: • 36.8 • 0.125 • 4.5

  10. Repeating Decimals • Repeating decimals are decimals that contain a infinite number of digits. • Examples: • 0.333… • 7.689689… FYI…The line above the decimals indicate that number repeats.

  11. Irrational Numbers • Irrational numbersare any numbers that cannot be expressed as a ratio, • They are expressed as non-terminating, non-repeating decimals; decimals that go on forever without repeating a pattern. • Examples of irrational numbers: • 0.34334333433334… • 45.86745893… • (pi)

  12. FYI…For Your Information • When taking the square root of any number that is not a perfect square, the resulting decimal will be non-terminating and non-repeating. Therefore, those numbers are always irrational.

  13. What are perfect squares? • 22 = 4 (√4 = 2) • 32 = 9 (√9 = 3) • 42 = 16 (√16 = 4) • 52 = 25 (√25 = 5) • 62 = 36 (√36 = 6) • 72 = 49 (√49 = 7) • 82 = 64 (√64 = 8)

  14. Examples of Nonperfect Squares • √2 = • √3 = • √7 = • √15 = • √22 = • √35 =

  15. Venn Diagram of the Real Number System Rational Numbers Irrational Numbers

  16. Example • Classify all the following numbers as natural, whole, integer, rational, or irrational. List all that apply. • 117 • 0 • -12.64039… • -½ • 6.36 • -3

  17. To show how these number are classified, use the Venn diagram. Place the number where it belongs on the Venn diagram. Rational Numbers Irrational Numbers Integers Whole Numbers Natural Numbers 0 -12.64039… 117 -3 6.36

  18. Solution • Now that all the numbers are placed where they belong in the Venn diagram, you can classify each number: • 117 is a natural number, a whole number, an integer, and a rational number. • is a rational number. • 0 is a whole number, an integer, and a rational number. • -12.64039… is an irrational number. • -3 is an integer and a rational number. • 6.36 is a rational number. • is an irrational number. • is a rational number.

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