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Classifying and Graphing Real Numbers

Learn how to identify and classify numbers in the real number system, including rational and irrational numbers. Practice graphing real numbers and comparing them.

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Classifying and Graphing Real Numbers

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  1. Transparency 3 Click the mouse button or press the Space Bar to display the answers.

  2. Splash Screen

  3. Example 3-7b Objective Identify and classify numbers in the real number system

  4. Example 3-7b Vocabulary Irrational number A number that cannot be expressed as a/b, where a and b are integers and b ≠ 0

  5. Example 3-7b Vocabulary Real number A set of rational and irrational numbers together

  6. Example 3-7b Review Vocabulary Rational number A number that can be expressed as a/b, where a and b are integers and b ≠ 0

  7. Example 3-7b Real Numbers Rational Numbers Irrational Numbers Integers Fractions, terminating and repeating decimals that are not integers Whole Numbers Negative Integers

  8. Lesson 3 Contents Example 1Classify Numbers Example 2Classify Numbers Example 3Classify Numbers Example 4Graph Real Numbers Example 5Compare Real Numbers Example 6Compare Real Numbers Example 7 Using Real Numbers

  9. Name all sets of numbers to which belongs. Example 3-1a Write problem Find the value of 5 Look at the graphic organizer for numbers 1/7

  10. Example 3-7b Real Numbers Real Numbers Rational Numbers Rational Numbers Irrational Numbers Integers Integers Fractions, terminating and repeating decimals that are not integers 5 Whole Numbers Whole Numbers Negative Integers Answer: Integer, Rational Number, Real Number Whole number, 1/7

  11. Name all sets of numbers to which belongs. Example 3-1b Answer: whole number, integer, rational number, real number 1/7

  12. Name all sets of numbers to which belongs. Example 3-2a Write problem Find the value of -3.464101615 . . . We have a repeating decimal that does NOT end 2/7

  13. Example 3-7b Real Numbers Real Numbers Irrational Numbers Rational Numbers Irrational Numbers -3.464101615 . . . Integers Fractions, terminating and repeating decimals that are not integers Whole Numbers Negative Integers Answer: Irrational Number, Real Number, 2/7

  14. Name all sets of numbers to which belongs. Example 3-2b Answer: irrational number, real number 2/7

  15. Example 3-3a Name all sets of numbers to which 0.090909… belongs. Write problem 0.090909 . . . The decimal ends in a repeating pattern. 3/7

  16. Example 3-7b Real Numbers Real Numbers Rational Numbers Rational Numbers Irrational Numbers 0.090909. . . Integers Fractions, terminating and repeating decimals that are not integers Fractions, terminating and repeating decimals that are not integers repeating decimals that are not integers Whole Numbers Negative Integers Answer: Repeating Decimal, Rational Number, Real Number, 3/7

  17. Example 3-3b Name all sets of numbers to which 0.1010101010… belongs. Answer: repeating decimal, rational number, real number 3/7

  18. Estimate and to the nearest hundredth. Then graph and on a number line. Example 3-4a Write problem Evaluate the expressions 2.8284 . . . -1.4142 . . . Round to nearest hundredth 2.83 -1.41 4/7

  19. Estimate and to the nearest hundredth. Then graph and on a number line. Example 3-4a Draw number line from at least -2 to 3 Plot solutions on number line 2.8284 . . . -1.4142 . . . Label with original expression 2.83 -1.41 Answer: 4/7

  20. Estimate and to the nearest tenth. Then graph and on a number line. Example 3-4b Answer: 4/7

  21. Replace with <, >, or to make a true sentence. Round to nearest hundredth Example 3-5a Write problem using a circle between the numbers Convert each to a decimal 3.875 3.872 Round to nearest hundredth Write a comparison 3.88 > 3.87 > Answer: 5/7

  22. Replace with <, >, or to make a true sentence. Answer: Example 3-5a > 5/7

  23. Replace with <, >, or to make a true sentence. Example 3-6a Write problem using a circle between the numbers Convert each to a decimal Must compare the thousandths position < 3.222 . . . 3.2249 Write a comparison Answer: < 6/7

  24. Replace with <, >, or to make a true sentence. Example 3-6b > Answer: 6/7

  25. BASEBALLThe time in seconds that it takes an object to fall d feet is How many seconds would it take for a baseball that is hit 250 feet straight up in the air to fall from its highest point to the ground? Example 3-7a Write the expression Replace d with 250 Follow order of operations P E MD AS 0.25 (15.81) Find the square root 3.95 Multiply Answer: 3.95 seconds 7/7

  26. BASEBALLThe time in seconds that it takes an object to fall d feet is How many seconds would it take for a baseball that is hit 450 feet straight up in the air to fall from its highest point to the ground? Example 3-7b * Answer: 5.31 seconds 7/7

  27. End of Lesson 3 Assignment

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