Lesson 5.1 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 b are both integers and b is not equal to 0. Problem Set Write each fraction as a decimal. 1. 1 5 0.25 2. 5 5 0.625 4 8 3. 23 5 0.23 4. 1 2 5 1.4 100 5 5. 3 7 16 5 3.4375 6. 12 15 5 12.46875 32 Graph each pair of rational numbers on the number line. Use the graph and write.,,, or 5 to compare the numbers. 7. 3 5. 0.25 0.25 0 0.1 0.2 0.3 3 5 0.4 0.5 0.6 0.7 0.8 0.9 1.0 8. 1.7. 1 5 8 5 1 1.7 8 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 Chapter 5 Skills Practice 523
Lesson 5.1 Skills Practice page 2 9. 0.09, 9 10 0.09 0 0.1 0.2 0.3 9 10 0.4 0.5 0.6 0.7 0.8 0.9 1.0 10. 4 3 4. 4.34 4.34 3 4 4 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 11. 11 16. 0.65 11 0.65 16 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 4 12. 3.8 5 3 4 5 3 5 3.8 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 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 41 natural numbers, whole numbers, or integers; closed under addition 14. 35 3 0 5 0 whole numbers or integers; closed under multiplication 15. 4 2 (23) 5 7 integers; closed under subtraction 16. 0 2 5 5 25 whole numbers are not closed under subtraction; closed under subtraction as integers 524 Chapter 5 Skills Practice
Lesson 5.1 Skills Practice page 3 Name Date 17. 9 2 11 5 22 natural numbers or whole numbers are not closed under subtraction; closed under subtraction as integers 18. 212 4 (25) 5 2 2 5 integers; not closed under division Add, subtract, multiply, or divide the rational numbers in each. 19. 27 1 13 5 6 20. 1 1 3 5 7 10 5 10 21. 4 1 2 2 3 5 2 1 22. 21.44 4 0.12 5 212 2 8 8 23. 2.40 3 (23.75) 5 29 24. 6 5 3 ( 2 7 12 ) 5 2 42 5 2 7 60 10 25. 5 4 1 5 20 3 4 5 6 2 26. 12.7 2 39.6 5 226.9 3 3 27. 27.82 2 (25.09) 5 22.73 28. 2 4 9 4 ( 2 32 27 ) 5 3 8 Chapter 5 Skills Practice 525
526 Chapter 5 Skills Practice
Lesson 5.2 Skills Practice Name Date Sew What? Irrational Numbers Vocabulary Match each term with the number that represents that term. 1. Irrational number a. 1 5 0.5 2 c 2. Terminating decimal b. 0. 3 a 3. Repeating decimal c. π d 4. Bar notation d. 5 5 0.555 9 b Problem Set Convert each fraction to a decimal and tell whether the fraction results in a terminating or repeating decimal. 1. 1 2. 7 25 9 0.04 0.7 7 25 ) 1.00 ; terminating 9 ) 7.00 ; repeating 3. 5 4. 5 12 8 0.416 6 0.625 12 ) 5.0000 ; repeating 8 ) 5.000 ; terminating 5. 13 6. 8 16 11 0.8125 0. 72 16 ) 13.0000 ; terminating 11 ) 8.00 ; repeating Chapter 5 Skills Practice 527
Lesson 5.2 Skills Practice page 2 Write each repeating decimal as a fraction. 7. 0.333 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 w 5 3 5 1 9 3 w 5 8 9 9. 0.0707 10. 0.5454 100w 5 7.07... 100w 5 54.54... 2w 5 0.07... 2w 5 0.54... 99w 5 7 99w 5 54 w 5 7 99 w 5 54 5 6 99 11 11. 0.1515 12. 0.2727 100w 5 15.15... 100w 5 27.27... 2w 5 0.15... 2w 5 0.27... 99w 5 15 99w 5 27 w 5 15 5 5 99 33 w 5 27 5 3 99 11 528 Chapter 5 Skills Practice
Lesson 5.2 Skills Practice page 3 Name Date 13. 0.298298 14. 0.185185 1000w 5 298.298... 1000w 5 185.185... 2w 5 0.298... 2w 5 0.185... 999w 5 298 999w 5 185 w 5 298 999 w 5 185 5 5 999 27 15. 0.67896789 16. 0.0243902439 10,000w 5 6789.6789... 100,000w 5 2439.02439... 2w 5 0.6789... 2w 5 0.02439... 9999w 5 6789 99,999w 5 2439 w 5 6789 5 2263 9999 3333 w 5 2439 5 1 99,999 41 Chapter 5 Skills Practice 529
Lesson 5.2 Skills Practice page 4 Tell whether each number is rational or irrational. 17. π 18. 4 irrational rational (2) 19. 18 20. 3 27 irrational rational (3) 21. 3 30 22. 1 49 irrational rational ( 1 7 ) 530 Chapter 5 Skills Practice
Lesson 5.3 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 the set is another member of the set. Problem Set Indicate whether each real number shown is rational, irrational, an integer, a whole number, a natural number, or some combination. 1. 35 2. 17 rational, integer, whole irrational number, natural number 3. 26 4. 5.25 rational, integer rational 5. 81 6. 2 2 3 rational, integer, whole number, natural number rational Chapter 5 Skills Practice 531
Lesson 5.3 Skills Practice page 2 7. 14 5 8. 0 7 rational rational, integer, whole number 9. 3 9 10. 2 16 3 8 irrational rational, integer Identify the property represented in each problem. 11. 18 3 1 5 18 12. 87 1 (259) 5 259 1 87 multiplicative identity commutative property of addition 13. 174 1 (2174) 5 0 14. If 1 1 1 2 2 5 1 and 4 ( 1 4 ) additive inverse transitive property of equality 5 1 then 1 1 1 2 2 5 4 ( 1 4 ) 15. 213 3 21 5 21 3 (213) 16. 2365 1 0 5 2365 commutative property of additive identity multiplication 17. 3 1 3 0.3 5 1 3 18. 245 1 (232 1 87) 5 [245 1 (232)] 1 87 multiplicative inverse associative property of addition 19. 567 5 567 20. If 2 3 4 5 20.75 then 20.75 5 2 3 4. reflexive property of equality symmetric property of equality 21. [5 3 (23)] 3 12 5 5 3 [(23) 3 12] 22. 2 4 1 0.8 5 0 5 associative property of multiplication additive inverse 532 Chapter 5 Skills Practice