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Algebra 1 Honors Unit 1.4 Classifying Real Numbers NOTES REAL NUMBERS Rational NUMBERS Irrational NUMBERS REAL NUMBERS Identify the category of Real Numbers each number best fits into. 1. 6 6. 2. -4 25 10. { 2 , , 5.196…} 3. 0 7. 3 4 11. {-10, 4. 7.5 8. {1,2,3,4,…} 3 , 3.3 , 7.745…, 25} Reference Glencoe Texbook: Page P7 Chapter 0-2 5. 9. {-8, 3, 7 16 , 9.1} 5 FINITE SET: Ex: {1, 2, 3, 4} Ex: {Natural Numbers less than 8} Ex: {Whole Numbers between 6 and 20} INFINITE SET: Ex: {…, 4, 5, 6,…} Ex: {3, 4, 5…} Ex: {Integers} Ex: {Whole numbers greater than 6} Determine if the number set is Finite or Infinite. 13. {The number of days in a year} F 15. I {Rational Numbers} F 14. I Reference Glencoe Texbook: Page P7 Chapter 0-2 {…-8, -6, -4, -2, 0} F 16. I {Natural Numbers less than 10} F I Algebra 1 Honors Unit 1.4 Classifying Real Numbers ASSIGNMENT 1. Fill in the table with set of numbers and words below that BEST describe each number group. (Not in random answer key!) Fractions {0, 1, 2, 3, …} Repeating Decimals {…, -1, 0, 1, …} Rational and Irrational Non-perfect Squares REAL 2. IRRATIONAL RATIONAL {1, 2, 3, …} INTEGERS Pi( ) Terminating Decimals Non-terminating Decimals WHOLE NATURAL Complete the chart. Put an “x” for each set to which the number belongs. You may be more than one “x” per problem. Problem Rational Integer Whole Natural Irrational 3 a 8 b 5 c -9 d 0 e f -1.5 g h 1 2 0.67 i 24 j -100 4 Reference Glencoe Texbook: Page P7 Chapter 0-2 True or False. If the statement is false, give a reason why. 3. All whole numbers are integers. ______ ____________________________ 4. All integers are rational. ______ 5. All decimals are irrational. ______ 6. All rational numbers are real. ______ ________________________________ 7. All square roots are irrational. ______ _______________________________ ___________________________________ ___________________________________ B and C Level Circle the letter that correctly describes each real number or number set given. 8. Negative five belongs to which number 9. Eight belongs to which number set(s) set(s) I. Whole II. Integer III. Real a. b. c. d. 10. I only I and II only III only II and III only Zero belongs to which number set(s) I. Natural II. Whole III. Integers a. b. c. d. II only I and II only II and III only I, II, and III Reference Glencoe Texbook: Page P7 Chapter 0-2 I. Natural II. Whole III. Integer a. b. c. d. I only I and II only II and III only I, II, and III 11. What set of numbers is represented by {…-4, -2, 0, 2, 4,...} a. b. c. d. Integers Whole Natural Irrational 12. What set of numbers is represented by { , 7 , 0.33 } a. b. c. d. 13. What set of numbers is 1 represented by {-4, , 0, 7, 8.5} 2 Rational Irrational Integer Real a. Integers b. Whole c. Rational d. Irrational In questions 14-17, Classify the following sets as: 14. 1 ,3,2.5,8 2 a. b. c. d. 16. 15. a. b. c. d. I II III V {0, 1, 2, 3, 4} a. b. c. d. 17. III II, III, IV II, III, IV, V All A Level 18. Describe the difference between a rational and irrational number. I. II. III. IV. V. {3, Irrational Numbers Rational Numbers Integers Whole Numbers Natural Numbers 5, 7, 9, 11} III, IV, V II, III, IV II, III, V All but I {-9, -6, -3, 0, 3, 6, 9} a. III b. II, III c. II, III, IV, V d. All 19. Describe the difference between an integer and whole number Reference Glencoe Texbook: Page P7 Chapter 0-2 20. Describe the difference between a natural number and a whole number. C Level In 21 – 32, Determine whether the following sets are finite or infinite. Finite: A set of numbers with both a beginning and end! Infinite: A set of numbers with no beginning and/or no end. 21. {natural numbers} 22. {Whole numbers} 23. {number of days in a week} 24. {Negative integers greater than -5} 25. {-5, -4, -3, -2} 26. {1, 2, 3, …, 14, 15, 16} 27. {Real Numbers} 28. {whole numbers between 0 and 9} 29. {…-2, -1, 0, 1, 2, …} 30. {Integers less than 5} 31. {natural numbers less than 27} 32. {Integers between –124 and 316} Directions: Create 3 examples for each type of number set below. B Level 33. Finite 34. Infinite Example 1: ______________________ Example 1: ______________________ Example 2: ______________________ Example 2: ______________________ Example 3: ______________________ Example 3: ______________________ A Level 35. Explain the difference between a finite and infinite set of numbers. Give an example for each type in your explanation. Reference Glencoe Texbook: Page P7 Chapter 0-2 Practice Assessments: 1.4 Assessment (Part 1) Level C 1C. –4 best fits into which category of Real Numbers? Level B Which of the following categories of Real Numbers does the number -2 fall into. 1B. a. Natural c. Irrational d. Rational a. b. c. d. e. 1.4 Assessment (Part 2) Level C Is the following set of whole numbers finite or infinite? Describe the difference between a Rational and Irrational Number. 1A. Circle every possible answer. b. Integer 2C. Level A Rational Irrational Integer Natural Whole Level B 2B. Create an example of a finite set. {…-2, -1, 0, 1,2…} Reference Glencoe Texbook: Page P7 Chapter 0-2 Level A Describe the difference between a finite and infinite set of numbers. Give an example of each type of set. 2A. ANSWERS: 1. Fill in the table with set of numbers and words below that BEST describe each number group. (Not in random answer key!) Fractions {0, 1, 2, 3, …} Repeating Decimals {…, -1, 0, 1, …} Rational and Irrational Non-perfect Squares REAL Rational And Irrational IRRATIONAL 2. Pi Non-Term. Dec. Non-Perfect Squares RATIONAL {1, 2, 3, …} INTEGERS Fractions Repeating Dec Term Dec {…-1,0,1} Pi( ) Terminating Decimals Non-terminating Decimals WHOLE {0,1,2,3…} NATURAL {1,2,3,…} Complete the chart. Put an “x” for each set to which the number belongs. You may be more than one “x” per problem. Problem Rational Integer Whole Natural Irrational 3 a x 8 b x 5 c -9 x x d 0 x x x e x f -1.5 x 1 g x 4 2 h x 0.67 i 24 x x x x j -100 x x True or False. If the statement is false, give a reason why. 3. All whole numbers are integers. __True__ ____________________________ 4. All integers are rational. _True_ ___________________________________ 5. All decimals are irrational. __False_ 6. All rational numbers are real. _True_ 7. All square roots are irrational. _False_ Reference Glencoe Texbook: Page P7 Chapter 0-2 Repeating and Term. Decimals are Rational ________________________________ Perfect Squares are rational Answers cont… 8. d 9. d 14. b 15. d 20. will vary 21. Inf 26. Fin 27. Inf 32. Fin 33. See examples in problems 2133. 10. c 16. b 22. Inf 28. Fin 34. See examples in problems 2133. 11. a 17. b 23. Fin 29. Inf 35. Fin-Sets terminate Infinite-Sets do not terminate 12. d 18. will vary 24. Fin 30. Inf 13. c 19. will vary 25. Fin 31. Inf Practice Assessments 1C b 1B a,c 1A 2C Infinite 2B 2A Rational numbers include all integers, fractions and terminating and repeating decimals. Irrational numbers only include nonterminating, nonrepeating decimals. Reference Glencoe Texbook: Page P7 Chapter 0-2 Answers Vary {1,2,3,4} Finite is a set of numbers that terminates (ends) {1,2,3,4} Infinite is a set of numbers that does not terminate. {…1,2,3,4…}