Lesson 1.1 Skills Practice Name_________________________________________________________ Date__________________________ So Many Numbers, So Little Time Number Sort Problem Set Provide a rationale for each grouping of numbers. ___ __ 64 , ___ 53 , 0.37 , 98% 1. __ 2 , p, √ 4 3 Answers will vary. These numbers are grouped together because they are all positive numbers. __ __ __ 2. p, 2√7 , √3 , √ 2 , 20.121221222 . . ., Answers will vary. These numbers are grouped together because they are all irrational numbers. ( ) 2 3. 8, __ 4 , 156.25, 2165 , 2401 5 Answers will vary. These numbers are grouped together because they can all be written using exponents. ( ) __ 2 6 , 12.9 4. __ 2 , 1.4545 . . ., ___ 74 , 25 __ 7 3 3 Answers will vary. © Carnegie Learning These numbers are grouped together because they are all repeating decimals. 5. 3, ___ 75 , 218, 2___ 30 5 3 Answers will vary. These numbers are grouped together because they are all integers. ___ __ 12 3 3 , 2√ 3 , 9 2 6. √ 81 , Answers will vary. These numbers are grouped together because they are all radicals. Chapter 1 Skills Practice • 303 462354_C3_Skills_CH01_303-318.indd 303 28/03/13 12:07 PM Lesson 1.1 Skills Practice page 2 List three numbers that satisfy each grouping. 7. mixed numbers 8. natural numbers Answers will vary. __ 4 , 2 ___ 17 , 1.3 Sample answer: 2 __ 5 3 9. numbers between 21 and 0 Answers will vary. __ Sample answer: 20.34, 2 2 , 20.5 3 Answers will vary. ___ ___ Sample answer: 124, √ 36 , 16 4 10. terminating decimals Answers will vary. __ __ Sample answer: 1 , 0.75, 21 3 5 2 11. improper fractions 12. irrational numbers Answers will vary. Answers will vary. Sample answer: 17 , 24 5 , 105% 5 8 Sample answer: √13 , p, 2√2 ___ __ © Carnegie Learning ___ __ 304 • Chapter 1 Skills Practice 462354_C3_Skills_CH01_303-318.indd 304 16/04/13 9:37 AM Lesson 1.2 Skills Practice Name_________________________________________________________ Date__________________________ Is It a Bird or a Plane? Rational Numbers Vocabulary Define each set of numbers in your own words. 1. Natural numbers Natural numbers consists of the numbers that you use to count objects. 2. Whole numbers Whole numbers are made up of the set of natural numbers and the number 0. 3. Integers Integers include all of the whole numbers and their additive inverses. 4. Closed A set of numbers is said to be closed when the operations could produce a defined value that is also in the set. 5. Rational numbers Rational numbers are numbers that can be written in the form __ a , where a and b are both b integers and b is not equal to 0. © Carnegie Learning Problem Set Write each fraction as a decimal. 1. __ 1 5 0.25 4 2. __ 5 5 0.625 8 23 5 0.23 3. ____ 100 2 5 1.4 4. 1 __ 5 7 5 3.4375 5. 3 ___ 16 15 5 12.46875 6. 12 ___ 32 Chapter 1 Skills Practice • 305 462354_C3_Skills_CH01_303-318.indd 305 28/03/13 12:07 PM Lesson 1.2 Skills Practice page 2 Graph each pair of rational numbers on the number line. Use the graph and write ., ,, or 5 to compare the numbers. 7. __ 3 . 0.25 5 3 5 0.25 0 0.1 0.2 0.3 0.4 0.5 5 8. 1.7 . 1 __ 8 0.6 0.7 1 1.0 1.1 1.2 9. 0.09 , ___ 9 10 1.3 1.4 1.5 0.8 0.9 1.0 1.8 2.0 5 1.7 8 1.6 1.7 9 10 0.09 0 0.1 1.9 0.2 0.3 3 . 4.34 10. 4 __ 4 0.4 0.5 0.6 0.7 4 4.34 4.0 4.1 4.2 4.3 4.4 4.5 4.6 11. ___ 11 . 0.65 16 0.8 0.9 1.0 3 4 4.7 4.8 4.9 5.0 11 0.65 16 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 © Carnegie Learning 0 4 5 3.8 3 4 12. 3.8 5 3 __ 5 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 306 • Chapter 1 Skills Practice 462354_C3_Skills_CH01_303-318.indd 306 28/03/13 12:07 PM Lesson 1.2 Skills Practice page 3 Name_________________________________________________________ Date__________________________ Tell whether the numbers in each problem are natural numbers, whole numbers, or integers, and identify whether those numbers are closed or open under the operation used. 13. 23 1 18 5 The numbers 23 and 18 are natural numbers, whole numbers, and integers. Natural numbers, whole numbers, and integers are closed under addition. 14. 35 3 0 5 The numbers 35 and 0 are whole numbers and integers. Whole numbers and integers are closed under multiplication. 15. 4 2 (23) 5 The numbers 4 and 23 are integers. Integers are closed under subtraction. 16. 0 2 5 5 The numbers 0 and 5 are whole numbers and integers. Whole numbers are not closed under subtraction. Integers are closed under subtraction. © Carnegie Learning 17. 9 2 11 5 The numbers 9 and 11 are natural numbers, whole numbers, and integers. Natural numbers and whole numbers are not closed under subtraction. Integers are closed under subtraction. 18. 212 4 (25) 5 The numbers 212 and 25 are integers. Integers are not closed under division. Chapter 1 Skills Practice • 307 462354_C3_Skills_CH01_303-318.indd 307 28/03/13 12:07 PM Lesson 1.2 Skills Practice page 4 Add, subtract, multiply, or divide the rational numbers in each. 19. 27 1 13 5 6 3 5 ___ 7 20. ___ 1 1 __ 10 5 10 3 5 2__ 1 2 2 __ 1 21. 4 __ 2 8 8 22. 21.44 4 0.12 5 212 23. 2.40 3 (23.75) 5 29 7 6 3 2___ 24. __ 5 2___ 42 5 2___ 7 12 5 60 10 1 5 ___ 2 20 5 6__ 25. __ 5 4 __ 3 4 3 3 26. 12.7 2 39.6 5 226.9 27. 27.82 2 (25.09) 5 22.73 32 4 5 __ 3 28. 2 __ 4 2___ 9 27 8 ( ) © Carnegie Learning ( ) 308 • Chapter 1 Skills Practice 462354_C3_Skills_CH01_303-318.indd 308 28/03/13 12:07 PM Lesson 1.3 Skills Practice Name_________________________________________________________ Date__________________________ Sew What? Irrational Numbers Vocabulary Match each term with the number that represents that term. 1 5 0.5 a. __ 2 1. Irrational number c __ 2. Terminating decimal b. 0.3 a 3. Repeating decimal c. π d 5 5 0.555… d. __ 9 4. Bar notation b Problem Set Convert each fraction to a decimal. State whether the fraction is equivalent to a terminating or repeating decimal. 2. __ 7 9 © Carnegie Learning 1. ___ 1 25 __ 0.04 _____ 25)1.00 0.77 _____ 9)7.00 1 is equivalent to The fraction ___ 25 the terminating decimal 0.04. The fraction __ 7 is equivalent to __ 9 the repeating decimal 0.77 . 3. ___ 5 12 __ 4. __ 5 8 0.4166 _______ ) 125.0000 0.625 ______ ) 85.000 5 is equivalent to The fraction ___ __ 12 the repeating decimal 0.4166 . The fraction __ 5 is equivalent to 8 the terminating decimal 0.625. Chapter 1 Skills Practice • 309 462354_C3_Skills_CH01_303-318.indd 309 28/03/13 12:07 PM Lesson 1.3 Skills Practice page 2 6. ___ 8 11 5. ___ 13 16 ___ 0.8125 ________ 16)13.0000 0.72 _____ 11)8.00 13 is equivalent to The fraction ___ 16 the terminating decimal 0.8125. The fraction ___ 8 is equivalent to 11 ___ the repeating decimal 0.72 . Write each repeating decimal as a fraction. 8. 0.888 … 10w 5 3.33... 10w 5 8.88... 2w 5 0.33... 2w 5 0.88... 9w 5 3 9w 5 8 1 w 5 __ 3 5 __ 9 3 9. 0.0707 … 100w 5 7.07... 2w 5 0.07... 99w 5 7 w 5 ___ 7 99 8 w 5 __ 9 10. 0.5454 … 100w 5 54.54... 2w 5 0.54... 99w 5 54 w 5 ___ 54 5 ___ 6 99 11 © Carnegie Learning 7. 0.333 … 310 • Chapter 1 Skills Practice 462354_C3_Skills_CH01_303-318.indd 310 28/03/13 12:07 PM Lesson 1.3 Skills Practice page 3 Name_________________________________________________________ Date__________________________ 11. 0.1515 … 100w 5 15.15... 100w 5 27.27... 2w 5 0.15... 2w 5 0.27... 99w 5 15 5 w 5 ___ 15 5 ___ 99 33 13. 0.298298 … 99w 5 27 w 5 ___ 27 5 ___ 3 99 11 14. 0.185185 … 1000w 5 298.298... 1000w 5 185.185... 2w 5 0.298... 2w 5 0.185... 999w 5 298 w 5 ____ 298 999 15. 0.67896789… 10,000w 5 6789.6789... © Carnegie Learning 12. 0.2727 … 2w 5 0.6789... 9999w 5 6789 5 _____ 2263 w 5 _____ 6789 9999 3333 999w 5 185 w 5 ____ 185 5 ___ 5 999 27 16. 0.0243902439 … 100,000w 5 2439.02439... 2w 5 0.02439... 99,999w 5 2439 2439 w 5 _______ 5 ___ 1 99,999 41 Chapter 1 Skills Practice • 311 462354_C3_Skills_CH01_303-318.indd 311 28/03/13 12:07 PM Lesson 1.3 Skills Practice page 4 Calculate the square root for each perfect square. ___ __ 17. √ 25 18. √ 9 25 5 5 3 5 95333 √25 5 √ 52 √9 5 √ 32 __ ___ 55 ___ __ __ 53 ____ 19. √ 49 20. √225 49 5 7 3 7 225 5 15 3 15 √49 5 √ 72 √225 5 √ 152 __ ___ 57 ____ ____ 5 15 ____ ____ 22. √ 625 21. √900 900 5 30 3 30 625 5 25 3 25 √900 5 √ 30 √625 5 √252 ____ ____ 2 5 30 ____ ____ 5 25 Use a calculator to calculate each square root to the nearest thousandth. ____ 25. √ 360 5 18.974 _____ 27. √ 236 5 cannot evaluate ___ 24.√3.6 5 1.897 _____ 26.√0.36 5 0.6 _____ 28.√ 3600 5 60 © Carnegie Learning ___ 23. √ 36 5 6 312 • Chapter 1 Skills Practice 462354_C3_Skills_CH01_303-318.indd 312 28/03/13 12:07 PM Lesson 1.3 Skills Practice page 5 Name_________________________________________________________ Date__________________________ Estimate each square root to the nearest tenth. ___ ___ 30. √ 38 29. √ 14 __ ___ ___ ___ ___ __ ___ __ 38 , √ 49 √36 , √ √32 , √ 14 , √ 42 √62 , √ 38 , √ 72 3,√ 14 , 4 6,√ 38 , 7 (3.7)(3.7) 5 13.69 (6.1)(6.1) 5 37.21 (3.8)(3.8) 5 14.44 (6.2)(6.2) 5 38.44 √14 < 3.7 √38 < 6.2 __ __ ___ ___ ___ ___ ___ ___ __ 32. √ 22 31. √ 7 __ __ __ ___ ___ ___ __ ___ __ 7 , √ 9 √4 , √ 22 , √ 25 √16 , √ √22 , √ 7 , √ 32 √42 , √ 22 , √ 52 2,√ 7 , 3 4,√ 22 , 5 (2.6)(2.6) 5 6.76 (4.6)(4.6) 5 21.16 (2.7)(2.7) 5 7.29 (4.7)(4.7) 5 22.09 √7 < 2.6 √22 < 4.7 __ __ __ __ __ ___ ___ ___ ____ 33. √ 93 34. √ 147 ___ ___ __ ___ ____ ____ ____ ____ 93 , √ 100 √81 , √ 147 , √ 169 √144 , √ √92 , √ 93 , √ 102 √122 , √ 147 , √ 132 9,√ 93 , 10 12 , √ 147 , 13 (9.6)(9.6) 5 92.16 (12.1)(12.1) 5 146.41 (9.7)(9.7) 5 94.09 (12.2)(12.2) , 148.84 √93 < 9.6 √147 < 12.1 ____ ___ © Carnegie Learning ___ 14 , √ 16 √9 , √ ___ ____ ____ ____ ____ ____ Chapter 1 Skills Practice • 313 462354_C3_Skills_CH01_303-318.indd 313 16/04/13 9:38 AM © Carnegie Learning 314 • Chapter 1 Skills Practice 462354_C3_Skills_CH01_303-318.indd 314 28/03/13 12:07 PM Lesson 1.4 Skills Practice Name_________________________________________________________ Date__________________________ Worth 1000 Words Real Numbers and Their Properties Vocabulary Write a description of each term in your own words. 1. real numbers The set of real numbers is the combined set of rational numbers and irrational numbers. 2. Venn diagram A Venn diagram is a diagram used to show how sets overlap. 3. closed (under an operation) A set of numbers is closed under an operation if the result of the operation on two numbers in © Carnegie Learning the set is another member of the set. Chapter 1 Skills Practice • 315 462354_C3_Skills_CH01_303-318.indd 315 28/03/13 12:07 PM Lesson 1.4 Skills Practice page 2 Problem Set Use the following number set to answer each question. __ ___ ___ √12 3 , 2 ___ p, 5.65, 2 __ 1 , √7 , 135%, 212, 42 , |29|, 4.56 , 22.24 ? 103 , 2 __ 18 , ___ 3 , 283 , 95%, 20.1, 0, __ 2 , |6|, 22 4 8 1. List the positive numbers. ___ __ √___ ___ 6 3 __ __ p, 5.65, √ 7 , 135%, 42, |29|, 4.56 , 2 3 , 3 , 95%, 2 , |6|, 22 4 12 3 2. Order the numbers from least to greatest. ___ ___ __ 18 1 22.24 ? 103 , 283 , 212, 2 , 2 , 20.1, 0, 3 , 2 , 95%, 135%, √ 7 , 2 3 , p, 4.56 , 5.65, |6|, |29|, 6 8 4 12 3 42 , 22 ___ __ 3. List the integers. √___ __ __ ___ 18 212, 42, |29|, 22.24 ? 103 , 2 , 0, 283 , |6|, 22 6 4. List the irrational numbers. __ p, √7 5. List the real numbers. All of the numbers are real numbers. ___ ___ 18 1 √__ 3 2 3 p, 5.65, 2 , 7 , 135%, 212, 4 , 4.56 , 22.24 ? 10 , 2 , 2 , 3 , 283 , 95%, 20.1, 0, 2 , |6|, 22 8 6 4 12 3 6. List the whole numbers. 2 , |29|, 0, |6|, 22 4 __ ___ √___ __ © Carnegie Learning __ 316 • Chapter 1 Skills Practice 462354_C3_Skills_CH01_303-318.indd 316 28/03/13 12:07 PM Lesson 1.4 Skills Practice page 3 Name_________________________________________________________ Date__________________________ Indicate whether each real number shown is rational, irrational, an integer, a whole number, a natural number, or some combination. 7. 35 rational, integer, whole ___ 8.√17 irrational number, natural number 9. 26 rational, integer ___ 11.√81 rational, integer, whole 10. 5.25 rational 2 12. 2 __ 3 rational number, natural number 14 13. ___ 5 rational 0 14. __ 7 rational, integer, whole number © Carnegie Learning ___ 3 15. 9 irrational √ 16 16. 2 ____ 3 8 rational, integer Chapter 1 Skills Practice • 317 462354_C3_Skills_CH01_303-318.indd 317 28/03/13 12:07 PM Lesson 1.4 Skills Practice page 4 Identify the property represented in each problem. 17. 18 3 1 5 18 multiplicative identity 19. 174 1 (2174) 5 0 additive inverse 21. 213 3 21 5 21 3 (213) commutative property of 18. 87 1 (259) 5 259 1 87 commutative property of addition ( ) ( ) 1 1 __ 1 5 1 then __ 1 1 __ 1 1 5 1 and 4__ 1 5 4__ 20. If __ 2 2 4 2 2 4 transitive property of equality 22. 2365 1 0 5 2365 additive identity multiplication 25. 567 5 567 reflexive property of equality 27. [5 3 (23)] 3 12 5 5 3 [(23) 3 12] associative property of multiplication 24. 245 1 (232 1 87) 5 [245 1 (232)] 1 87 associative property of addition 3 3 26. If 2 __ 5 20.75 then 20.75 5 2 __ . 4 4 symmetric property of equality 4 28. 2 __ 1 0.8 5 0 5 additive inverse © Carnegie Learning 1 3 0.3 5 1 23. 3 __ 3 multiplicative inverse 318 • Chapter 1 Skills Practice 462354_C3_Skills_CH01_303-318.indd 318 28/03/13 12:07 PM
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