9.2 rational and irrational numbers day 1

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9.2 rational and irrational numbers day 1

  1. 1. Write the fraction as a decimal. Lesson 9.2 , For use with pages 475-480 1. 4 5 2. 5 9
  2. 2. Write the fraction as a decimal. Lesson 9.2 , For use with pages 475-480 ANSWER 0.8 1. 4 5 2. 5 9 ANSWER 0.5
  3. 3. RATIONAL and IRRATIONAL NUMBERS 9.2
  4. 4. Essential Questions <ul><li>What is the difference between an irrational number and a rational number? </li></ul><ul><li>How are real numbers and the Pythagorean Theorem used in everyday life? </li></ul><ul><li>What types of real-life situations could the Pythagorean Theorem or square roots apply to? Why? </li></ul>
  5. 5. Rational Numbers <ul><li>Rational numbers are simply numbers that can be written as fractions or ratios </li></ul><ul><li>The hierarchy of real numbers looks something like this: </li></ul>
  6. 6. 1, 2, 3, 4, etc. 0, 1, 2, 3, 4, 5 .. –2, –1, 0, 1, 2, . Rational and irrational numbers Can be written as a fraction Can’t be written as a fraction
  7. 7. <ul><li>Rational Numbers : Any number that can be written in fraction form is a rational number . </li></ul><ul><ul><li>This includes integers, terminating decimals, and repeating decimals as well as fractions. </li></ul></ul>
  8. 8. <ul><li>An integer can be written as a fraction simply by giving it a denominator of one, so any integer is a rational number . </li></ul>
  9. 9. <ul><li>A terminating decimal can be written as a fraction simply by writing it the way you say it: 3.75 = three and seventy-five hundredths = </li></ul><ul><li>So, any terminating decimal is a rational number. </li></ul>
  10. 10. <ul><li>A repeating decimal can be written as a fraction using algebraic methods, so any repeating decimal is a rational number. </li></ul>
  11. 11. Irrational Numbers <ul><li>A number that cannot be expressed as a repeating or terminating decimal. </li></ul><ul><li>An integer that is not a perfect square has an irrational root. </li></ul><ul><li>REALS (the real numbers) </li></ul><ul><ul><li>The rational and irrational numbers. </li></ul></ul>
  12. 12. <ul><li>Rational Number </li></ul><ul><li>Fractions </li></ul><ul><li>Ratios </li></ul><ul><li>Whole numbers </li></ul><ul><li>Integers </li></ul><ul><li>Terminating decimals (stop) </li></ul><ul><li>Repeating decimals </li></ul><ul><li>Square root of a perfect square </li></ul><ul><li>Irrational Numbers </li></ul><ul><li>Non-terminating decimal </li></ul><ul><li>Non-repeating decimal </li></ul><ul><li>Square root of a number that is not a perfect square </li></ul>
  13. 13. GUIDED PRACTICE for Example 1 Tell whether the number is rational or irrational . Explain your reasoning. 5 8 1.
  14. 14. GUIDED PRACTICE for Example 1 Tell whether the number is rational or irrational . Explain your reasoning. 5 8 1. Rational because if we write it in its decimal form then it would be 0.625 which is terminating so it is a rational number ANSWER
  15. 15. GUIDED PRACTICE for Example 1 Tell whether the number is rational or irrational . Explain your reasoning. 2.
  16. 16. GUIDED PRACTICE for Example 1 Tell whether the number is rational or irrational . Explain your reasoning. 2. ANSWER Irrational because it is not a perfect square 2.64579131 . . . .
  17. 17. GUIDED PRACTICE for Example 1 Tell whether the number is rational or irrational . Explain your reasoning. 3.
  18. 18. GUIDED PRACTICE for Example 1 Tell whether the number is rational or irrational . Explain your reasoning. 3. ANSWER Rational because it is a perfect square
  19. 19. GUIDED PRACTICE for Example 1 Tell whether the number is rational or irrational . Explain your reasoning. 4. 2 9
  20. 20. GUIDED PRACTICE for Example 1 Tell whether the number is rational or irrational . Explain your reasoning. 4. 2 9 ANSWER Rational because if we write it in its decimal from then it would be 0.2 where 2 repeating so it is a rational number
  21. 21. EXAMPLE 1 Number Rational Rational Irrational Terminating Repeating Non terminating and non repeating Classifying Real Numbers Type Decimal Form Type of Decimal a. 3 4 b. 1 11 c. 3 11 1 = 0.0909… = 0.09 3 = 1.7320508 . . . 3 4 = 0.75 3
  22. 22. Examples <ul><li>Which of the following are irrational numbers? </li></ul>1. Irrational 2. Rational -30 3. Rational 74 4. Irrational
  23. 23. Homework <ul><li>Page 477 #1-15 </li></ul><ul><ul><li>Problems 3-14 will be two points each </li></ul></ul><ul><ul><ul><li>One point for rational or irrational </li></ul></ul></ul><ul><ul><ul><li>One point for the reason </li></ul></ul></ul>

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