Transcription
Chapter 8Resource Masters
Consumable WorkbooksMany of the worksheets contained in the Chapter Resource Masters bookletsare available as consumable workbooks in both English and Spanish.Study Guide and Intervention WorkbookStudy Guide and Intervention Workbook (Spanish)Skills Practice WorkbookSkills Practice Workbook (Spanish)Practice WorkbookPractice Workbook 07-827749-30-07-827748-50-07-827750-7ANSWERS FOR WORKBOOKS The answers for Chapter 8 of these workbookscan be found in the back of this Chapter Resource Masters booklet.Glencoe/McGraw-HillCopyright by The McGraw-Hill Companies, Inc. All rights reserved.Printed in the United States of America. Permission is granted to reproduce thematerial contained herein on the condition that such material be reproduced onlyfor classroom use; be provided to students, teachers, and families without charge;and be used solely in conjunction with Glencoe’s Algebra 1. Any other reproduction,for use or sale, is prohibited without prior written permission of the publisher.Send all inquiries to:The McGraw-Hill Companies8787 Orion PlaceColumbus, OH 43240-4027ISBN: 0-07-827732-92 3 4 5 6 7 8 9 10 024 11 10 09 08 07 06 05 04 03Algebra 1Chapter 8 Resource Masters
ContentsVocabulary Builder . . . . . . . . . . . . . . . . viiLesson 8-7Study Guide and Intervention . . . . . . . . 491–492Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 493Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 494Reading to Learn Mathematics . . . . . . . . . . 495Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 496Lesson 8-1Study Guide and Intervention . . . . . . . . 455–456Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 457Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 458Reading to Learn Mathematics . . . . . . . . . . 459Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 460Lesson 8-8Study Guide and Intervention . . . . . . . . 497–498Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 499Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 500Reading to Learn Mathematics . . . . . . . . . . 501Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 502Lesson 8-2Study Guide and Intervention . . . . . . . . 461–462Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 463Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 464Reading to Learn Mathematics . . . . . . . . . . 465Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 466Chapter 8 rLesson 8-3Study Guide and Intervention . . . . . . . . 467–468Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 469Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 470Reading to Learn Mathematics . . . . . . . . . . 471Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 472Lesson 8-4Study Guide and Intervention . . . . . . . . 473–474Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 475Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 476Reading to Learn Mathematics . . . . . . . . . . 477Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 4788 Test, Form 1 . . . . . . . . . . . . 503–5048 Test, Form 2A . . . . . . . . . . . 505–5068 Test, Form 2B . . . . . . . . . . . 507–5088 Test, Form 2C . . . . . . . . . . . 509–5108 Test, Form 2D . . . . . . . . . . . 511–5128 Test, Form 3 . . . . . . . . . . . . 513–5148 Open-Ended Assessment . . . . . . 5158 Vocabulary Test/Review . . . . . . . 5168 Quizzes 1 & 2 . . . . . . . . . . . . . . . 5178 Quizzes 3 & 4 . . . . . . . . . . . . . . . 5188 Mid-Chapter Test . . . . . . . . . . . . 5198 Cumulative Review . . . . . . . . . . . 5208 Standardized Test Practice . . 521–522Standardized Test PracticeStudent Recording Sheet . . . . . . . . . . . . . . A1Lesson 8-5Study Guide and Intervention . . . . . . . 479–480Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 481Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 482Reading to Learn Mathematics . . . . . . . . . . 483Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 484ANSWERS . . . . . . . . . . . . . . . . . . . . . . A2–A35Lesson 8-6Study Guide and Intervention . . . . . . . . 485–486Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 487Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 488Reading to Learn Mathematics . . . . . . . . . . 489Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 490 Glencoe/McGraw-HilliiiGlencoe Algebra 1
Teacher’s Guide to Using theChapter 8 Resource MastersThe Fast File Chapter Resource system allows you to conveniently file the resourcesyou use most often. The Chapter 8 Resource Masters includes the core materials neededfor Chapter 8. These materials include worksheets, extensions, and assessment options.The answers for these pages appear at the back of this booklet.All of the materials found in this booklet are included for viewing and printing in theAlgebra 1 TeacherWorks CD-ROM.Vocabulary BuilderPracticePages vii–viiiinclude a student study tool that presentsup to twenty of the key vocabulary termsfrom the chapter. Students are to recorddefinitions and/or examples for each term.You may suggest that students highlight orstar the terms with which they are notfamiliar.There is one master for eachlesson. These problems more closely followthe structure of the Practice and Applysection of the Student Edition exercises.These exercises are of average difficulty.WHEN TO USE These provide additionalpractice options or may be used ashomework for second day teaching of thelesson.WHEN TO USE Give these pages tostudents before beginning Lesson 8-1.Encourage them to add these pages to theirAlgebra Study Notebook. Remind them toadd definitions and examples as theycomplete each lesson.Reading to Learn MathematicsOne master is included for each lesson. Thefirst section of each master asks questionsabout the opening paragraph of the lessonin the Student Edition. Additionalquestions ask students to interpret thecontext of and relationships among termsin the lesson. Finally, students are asked tosummarize what they have learned usingvarious representation techniques.Study Guide and InterventionEach lesson in Algebra 1 addresses twoobjectives. There is one Study Guide andIntervention master for each objective.WHEN TO USE Use these masters asWHEN TO USE This master can be usedreteaching activities for students who needadditional reinforcement. These pages canalso be used in conjunction with the StudentEdition as an instructional tool for studentswho have been absent.as a study tool when presenting the lessonor as an informal reading assessment afterpresenting the lesson. It is also a helpfultool for ELL (English Language Learner)students.Skills PracticeThere is one master foreach lesson. These provide computationalpractice at a basic level.EnrichmentThere is one extensionmaster for each lesson. These activities mayextend the concepts in the lesson, offer anhistorical or multicultural look at theconcepts, or widen students’ perspectives onthe mathematics they are learning. Theseare not written exclusively for honorsstudents, but are accessible for use with alllevels of students.WHEN TO USE These masters can beused with students who have weakermathematics backgrounds or needadditional reinforcement.WHEN TO USE These may be used asextra credit, short-term projects, or asactivities for days when class periods areshortened. Glencoe/McGraw-HillivGlencoe Algebra 1
Assessment OptionsIntermediate AssessmentThe assessment masters in the Chapter 8Resources Masters offer a wide range ofassessment tools for intermediate and finalassessment. The following lists describe eachassessment master and its intended use. Four free-response quizzes are includedto offer assessment at appropriateintervals in the chapter. A Mid-Chapter Test provides an optionto assess the first half of the chapter. It iscomposed of both multiple-choice andfree-response questions.Chapter AssessmentCHAPTER TESTSContinuing Assessment Form 1 contains multiple-choice questionsand is intended for use with basic levelstudents. The Cumulative Review providesstudents an opportunity to reinforce andretain skills as they proceed throughtheir study of Algebra 1. It can also beused as a test. This master includesfree-response questions. Forms 2A and 2B contain multiple-choicequestions aimed at the average levelstudent. These tests are similar in formatto offer comparable testing situations. The Standardized Test Practice offerscontinuing review of algebra concepts invarious formats, which may appear onthe standardized tests that they mayencounter. This practice includes multiplechoice, grid-in, and quantitativecomparison questions. Bubble-in andgrid-in answer sections are provided onthe master. Forms 2C and 2D are composed of freeresponse questions aimed at the averagelevel student. These tests are similar informat to offer comparable testingsituations. Grids with axes are providedfor questions assessing graphing skills. Form 3 is an advanced level test withfree-response questions. Grids withoutaxes are provided for questions assessinggraphing skills.AnswersAll of the above tests include a freeresponse Bonus question. Page A1 is an answer sheet for theStandardized Test Practice questionsthat appear in the Student Edition onpages 470–471. This improves students’familiarity with the answer formats theymay encounter in test taking. The Open-Ended Assessment includesperformance assessment tasks that aresuitable for all students. A scoring rubricis included for evaluation guidelines.Sample answers are provided forassessment. The answers for the lesson-by-lessonmasters are provided as reduced pageswith answers appearing in red. A Vocabulary Test, suitable for allstudents, includes a list of the vocabularywords in the chapter and ten questionsassessing students’ knowledge of thoseterms. This can also be used in conjunction with one of the chapter tests or as areview worksheet. Glencoe/McGraw-Hill Full-size answer keys are provided forthe assessment masters in this booklet.vGlencoe Algebra 1
NAME DATE8PERIODReading to Learn MathematicsThis is an alphabetical list of the key vocabulary terms you will learn in Chapter 8.As you study the chapter, complete each term’s definition or description.Remember to add the page number where you found the term. Add these pages toyour Algebra Study Notebook to review vocabulary at the end of the chapter.Vocabulary TermFoundon PageDefinition/Description/Example binomialby·NOH·mee·uhlconstantdegree of a monomialdegree of a polynomialFOIL method monomialmah·NOH·mee·uhlnegative exponent polynomialPAH·luh·NOH·mee·uhl(continued on the next page) Glencoe/McGraw-HillviiGlencoe Algebra 1Vocabulary BuilderVocabulary Builder
NAME DATE8PERIODReading to Learn MathematicsVocabulary BuilderVocabulary Term(continued)Foundon PageDefinition/Description/ExamplePower of a PowerPower of a ProductProduct of PowersPower of a QuotientQuotient of Powersscientific notation trinomialtry·NOH·mee·uhlzero exponent Glencoe/McGraw-HillviiiGlencoe Algebra 1
NAME DATE8-16-1PERIODStudy Guide and InterventionMultiplying MonomialsMultiply MonomialsA monomial is a number, a variable, or a product of a numberand one or more variables. An expression of the form xn is called a power and representsthe product you obtain when x is used as a factor n times. To multiply two powers that havethe same base, add the exponents.Example 1Example 2Simplify (3x6)(5x2).(3x6)(5x2) (3)(5)(x6 x2) (3 5)(x6 2) 15x8Simplify ( 4a3b)(3a2b5).( 4a3b)(3a2b5) ( 4)(3)(a3 a2)(b b5) 12(a3 2)(b1 5) 12a5b6Associative PropertyProduct of PowersSimplify.The product is 15x8.The product is 12a5b6.ExercisesSimplify.1. y( y5)2. n2 n73. ( 7x2)(x4)4. x(x2)(x4)5. m m56. ( x3)( x4)7. (2a2)(8a)8. (rs)(rs3)(s2)9. (x2y)(4xy3)1310. (2a3b)(6b3) 15 13. (5a2bc3) abc4 Glencoe/McGraw-Hill11. ( 4x3)( 5x7)12. ( 3j 2k4)(2jk6)14. ( 5xy)(4x2)( y4)15. (10x3yz2)( 2xy5z)455Glencoe Algebra 1Lesson 8-1For any number a and all integers m and n, am an a m n.Product of Powers
NAME DATE8-1PERIODStudy Guide and Intervention(continued)Multiplying MonomialsPowers of MonomialsAn expression of the form (xm) n is called a power of a powerand represents the product you obtain when x m is used as a factor n times. To find thepower of a power, multiply exponents.Power of a PowerFor any number a and all integers m and n, (am) n amn.Power of a ProductFor any number a and all integers m and n, (ab) m amb m.Example( 2ab2)3(a2)4 Simplify ( 2ab2)3(a2)4.( 2ab2)3(a8)( 2)3(a3)(b2)3(a8)( 2)3(a3)(a8)(b2)3( 2)3(a11)(b2)3 8a11b6Power of a PowerPower of a ProductCommutative PropertyProduct of PowersPower of a PowerThe product is 8a11b6.ExercisesSimplify.1. (y5) 22. (n7) 43. (x2) 5(x3)4. 3(ab4) 35. ( 3ab4) 36. (4x2b) 37. (4a2)2(b3)8. (4x) 2(b3)9. (x2 y 4) 510. (2a3b2)(b3) 2 15 13. (25a2b) 3 abc216. ( 2n6y5)( 6n3y2)(ny) 3 Glencoe/McGraw-Hill11. ( 4xy)3( 2x2)312. ( 3j 2k3) 2(2j 2k) 314. (2xy)2( 3x2)(4y4)15. (2x3y2z2)3(x2z)417. ( 3a3n4)( 3a3n) 418. 3(2x) 4(4x5y)2456Glencoe Algebra 1
NAME DATE8-1PERIODSkills PracticeMultiplying MonomialsDetermine whether each expression is a monomial. Write yes or no. Explain.1. 112. a bp2q3. 2Lesson 8-14. y5. j 3k6. 2a 3bSimplify.7. a2(a3)(a6)8. x(x2)(x7)9. (y2z)(yz2)10. ( 2k2)( 3k)11. (e2f 4)(e2f 2)12. (cd2)(c3d2)13. (2x2)(3x5)14. (5a7)(4a2)15. (4xy3)(3x3y5)16. (7a5b2)(a2b3)17. ( 5m3)(3m8)18. ( 2c4d)( 4cd)19. (102)320. (p3)1221. ( 6p)222. ( 3y)323. (3pq2)224. (2b3c4)2GEOMETRY Express the area of each figure as a monomial.25.26.27.x2cd4px5 Glencoe/McGraw-Hillcd9p 3457Glencoe Algebra 1
NAME DATE8-1PERIODPracticeMultiplying MonomialsDetermine whether each expression is a monomial. Write yes or no. Explain.21a27b1. b3c222. Simplify.3. ( 5x2y)(3x4)4. (2ab2c2)(4a3b2c2)5. (3cd4)( 2c2)6. (4g3h)( 2g5) 137. ( 15xy4) xy3 168. ( xy)3(xz) 9. ( 18m2n)2 mn210. (0.2a2b3)2 23 12. cd313. (0.4k3)314. [(42)2]211. p 14 22GEOMETRY Express the area of each figure as a monomial.15.16.17.5x 33ab 26ac 36a 2b 44a 2cGEOMETRY Express the volume of each solid as a monomial.18.19.n3h 2mn 3m 3n20.3g7g 23h 23h 221. COUNTING A panel of four light switches can be set in 24 ways. A panel of five lightswitches can set in twice this many ways. In how many ways can five light switchesbe set?22. HOBBIES Tawa wants to increase her rock collection by a power of three this year andthen increase it again by a power of two next year. If she has 2 rocks now, how manyrocks will she have after the second year? Glencoe/McGraw-Hill458Glencoe Algebra 1
NAME DATE8-1PERIODReading to Learn MathematicsMultiplying MonomialsPre-ActivityWhy does doubling speed quadruple braking distance?Read the introduction to Lesson 8-1 at the top of page 410 in your textbook.Find two examples in the table to verify the statement that when speed isdoubled, the braking distance is quadrupled. Write your examples in thetable.Braking Distance(feet)Speed Doubled(miles per hour)Braking DistanceQuadrupled (feet)Lesson 8-1Speed(miles per hour)Reading the Lesson1. Describe the expression 3xy using the terms monomial, constant, variable, and product.2. Complete the chart by choosing the property that can be used to simplify eachexpression. Then simplify the expression.ExpressionPropertyExpression SimplifiedProduct of Powers35 32Power of a PowerPower of a ProductProduct of Powers(a 3)4Power of a PowerPower of a ProductProduct of Powers( 4xy)5Power of a PowerPower of a ProductHelping You Remember3. Write an example of each of the three properties of powers discussed in this lesson.Then, using the examples, explain how the property is used to simplify them. Glencoe/McGraw-Hill459Glencoe Algebra 1
NAME DATE8-1PERIODEnrichmentAn WangAn Wang (1920–1990) was an Asian-American who became one of thepioneers of the computer industry in the United States. He grew up inShanghai, China, but came to the United States to further his studiesin science. In 1948, he invented a magnetic pulse controlling devicethat vastly increased the storage capacity of computers. He laterfounded his own company, Wang Laboratories, and became a leader inthe development of desktop calculators and word processing systems.In 1988, Wang was elected to the National Inventors Hall of Fame.Digital computers store information as numbers. Because theelectronic circuits of a computer can exist in only one of two states,open or closed, the numbers that are stored can consist of only twodigits, 0 or 1. Numbers written using only these two digits are calledbinary numbers. To find the decimal value of a binary number, youuse the digits to write a polynomial in 2. For instance, this is how tofind the decimal value of the number 10011012. (The subscript2 indicates that this is a binary number.)10011012 1 26 0 25 0 24 1 23 1 22 0 21 1 20 1 6432168 1 4 0 2 1 1 0 0 1 64 0 0 8 4 0 1 77Find the decimal value of each binary number.1. 111122. 1000023. 1100001124. 101110012Write each decimal number as a binary number.5. 86. 117. 299. The chart at the right shows a set of decimalcode numbers that is used widely in storingletters of the alphabet in a computer's memory.Find the code numbers for the letters of yourname. Then write the code for your nameusing binary numbers. Glencoe/McGraw-Hill4608. 117The American Standard Guide forInformation Interchange 111112113114115116117118119120121122Glencoe Algebra 1
NAME DATE8-26-2PERIODStudy Guide and InterventionDividing MonomialsQuotients of MonomialsTo divide two powers with the same base, subtract theexponents.amaQuotient of PowersFor all integers m and n and any nonzero number a, am n.nPower of a QuotientFor any integer m and any real numbers a and b, b 0, a4b7abExample 2Simplify . Assume2neither a nor b is equal to zero. a4b7a4 b7 2 2a bab (a4 1)(b7 2) a3b5The quotient is a3b5 .mamb .m3 5 3 2a3bb Simplify .2Assume that b is not equal to zero.2a b 3b 3 5 3Group powers with the same base.2Quotient of Powers(2a3b5)3(3b )Power of a Quotient23(a3)3(b5)3(3) (b )Power of a Product8a9b1527bPower of a Power8a9b927Quotient of Powers 2 3 3 2 3Simplify. 6 8a9b927The quotient is .ExercisesSimplify. Assume that no denominator is equal to zero.5552. 4a2a5. 5 2xy6y x8. 1. 24. p5n4p nx5y3x y6. 52 2vv ww 3 410. 4 3 3. 2 2y714y 2aa b 7. 45m6mGlencoe/McGraw-Hillq 4p3p q 4 4 339. 2 2 3r2r ss 6 3 4r7s7t 2s r t11. 512. 3 3 2461Glencoe Algebra 1Lesson 8-2Example 1 ab
NAME DATE8-2PERIODStudy Guide and Intervention(continued)Dividing MonomialsNegative ExponentsAny nonzero number raised to the zero power is 1; for example,( 0.5)0 1. Any nonzero number raised to a negative power is equal to the reciprocal of the1number raised to the opposite power; for example, 6 3 3 . These definitions can be used6to simplify expressions that have negative exponents.Zero ExponentFor any nonzero number a, a0 1.Negative Exponent PropertynFor any nonzero number a and any integer n, a n n a .n and 1a1aThe simplified form of an expression containing negative exponents must contain onlypositive exponents.4a 3b616a b cExampleSimplify 2 6 5 . Assume that the denominator is not equal to zero.14a 3b64a 3 b6 526 526c1616a b cab Group powers with the same base.14Quotient of Powers and Negative Exponent Properties14Simplify. (a 3 2)(b6 6)(c5) a 5b0c5 1 14 aNegative Exponent and Zero Exponent Propertiesc54aSimplify. 5 (1)c5 5c54aThe solution is 5 .ExercisesSimplify. Assume that no denominator is equal to zero.2221. 33. 3( x 1 y)04w y6. 2(6a 1b)2(b )9. 1 2 74. 5b 4b5. 1 2x4 y0x8. 2 47. 2s 3t 5(s t )10. 2 3 1 p 8pmm2. 4Glencoe/McGraw-Hill (a2b3)2(ab)(3st)2u 4s t u( 2mn2) 34m n 4m2n2 08m 11. 112. 6 4462Glencoe Algebra 1
NAME DATE8-2PERIODSkills PracticeDividing MonomialsSimplify. Assume that no denominator is equal to zero.6562. 891293. 2x4x4. 3 4mm6. 612n536n8. 4a3b5ab10. 3 2 21w5u27w u12. 213. 2 4p7s 14. 4 415. 8 216. 1. 4r3s2r s9d73d7. 9. 211. 4 57 2 9 111w4u3w um7n2m n32x3y2z5 8xyz 35 2h317. 18. h 619. k0(k4)(k 6)20. k 1( 6)(m3)f 7f22. 3 3f 5g 4h24. 5xy 11 15w0u 15u26. 5 621. 423. 225. 3 Glencoe/McGraw-HillLesson 8-25. 3q 16p2p q 5 2 015x6y 948x6y7z5 6xy z463Glencoe Algebra 1
NAME DATE8-2PERIODPracticeDividing MonomialsSimplify. Assume that no denominator is equal to zero.8882. 3m5npm p5. 21. 44. 4 4f3hg 37. 6310. x3( y 5)(x 8)a4b6ab3. xy2xy5c2d3 4c d6. 6 58y7z64y z 7p6ws 58. 6 3 4c224c29. 511. p(q 2)(r 3)22r3s211r s 73 14. 15w0u 15u17. 1 2 36f 2g3h554f g h20. 3513. 216. 319. 2 5 3m 2n 522. (m4n3) 1q 1r 3 5 qr 25. 212. 12 2 43 15. 2 38c3d2f 44c d f18. 3 12t 1u5v 42t uv21. 3( j 1k3) 4j k24. 2 4 4x 3y5 0 4 r4(3r)(2a 2b) 35a b23. 3 37c 3d 3 1 c de 26. 5 42x3y2z 2 3x yz 27. 4 228. BIOLOGY A lab technician draws a sample of blood. A cubic millimeter of the bloodcontains 223 white blood cells and 225 red blood cells. What is the ratio of white bloodcells to red blood cells?29. COUNTING The number of three-letter “words” that can be formed with the Englishalphabet is 263. The number of five-letter “words” that can be formed is 265. How manytimes more five-letter “words” can be formed than three-letter “words”? Glencoe/McGraw-Hill464Glencoe Algebra 1
NAME DATE8-2PERIODReading to Learn MathematicsDividing MonomialsPre-ActivityHow can you compare pH levels?Read the introduction to Lesson 8-2 at the top of page 417 in your textbook. 101 In the formula c pH, identify the base and the exponent. How do you think c will change as the exponent increases?Reading the Lessonamam n means.1. Explain what the statement n a 101 pH, you can find the power of the numerator, the power ofLesson 8-22. To find c in the formula c the denominator, and divide. This is an example of what property?3. Use the Quotient of Powers Property to explain why 30 1.4. Consider the expression 4 3.a. Explain why the expression 4 3 is not simplified.b. Define the term reciprocal.c. 4 3 is the reciprocal of what power of 4?d. What is the simplified form of 4 3?Helping You Remember4x22x5. Describe how you would help a friend who needs to simplify the expression 5 . Glencoe/McGraw-Hill465Glencoe Algebra 1
NAME DATE8-2PERIODEnrichmentPatterns with PowersUse your calculator, if necessary, to complete each pattern.a. 210 b. 510 c. 410 29 59 49 28 58 48 27 57 47 26 56 46 25 55 45 24 54 44 23 53 43 22 52 42 21 51 41 Study the patterns for a, b, and c above. Then answer the questions.1. Describe the pattern of the exponents from the top of each column to the bottom.2. Describe the pattern of the powers from the top of the column to the bottom.3. What would you expect the following powers to be?2050404. Refer to Exercise 3. Write a rule. Test it on patterns that you obtain using 22, 25, and 24as bases.Study the pattern below. Then answer the questions.03 0 02 0 01 0 00 ?0 1 does not exist. 0 2 does not exist. 0 3 does not exist.5. Why do 0 1, 0 2, and 0 3 not exist?6. Based upon the pattern, can you determine whether 00 exists?7. The symbol 00 is called an indeterminate, which means that it has no unique value.Thus it does not exist as a unique real number. Why do you think that 00 cannot equal 1? Glencoe/McGraw-Hill466Glencoe Algebra 1
NAME DATE8-36-3PERIODStudy Guide and InterventionScientific NotationScientific Notation Keeping track of place value in very large or very small numberswritten in standard form may be difficult. It is more efficient to write such numbers inscientific notation. A number is expressed in scientific notation when it is written as aproduct of two factors, one factor that is greater than or equal to 1 and less than 10 and onefactor that is a power of ten.Scientific NotationA number is in scientific notation when it is in the form a 10n, where 1 a 10and n is an integer.Example 1Example 2Express 3.52 104 instandard notation.Express 6.21 10 5 instandard notation.3.52 104 3.52 10,000 35,2006.21 10 5 6.21 5110 6.21 0.00001 0.0000621The decimal point moved 5 places to the left.The decimal point moved 4 places to theright.Example 3Example 4Express 0.0000549 inscientific notation.37,600,000 3.76 107The decimal point moved 7 places so that itis between the 3 and the 7. Since37,600,000 1, the exponent is positive.0.0000549 5.49 10 5The decimal point moved 5 places so that itis between the 5 and the 4. Since0.0000549 1, the exponent is negative.Lesson 8-3Express 37,600,000 inscientific notation.ExercisesExpress each number in standard notation.1. 3.65 1052. 7.02 10 43. 8.003 1084. 7.451 1065. 5.91 1006. 7.99 10 17. 8.9354 10108. 8.1 10 99. 4 1015Express each number in scientific notation.10. 0.000045611. 0.0000112. 590,000,00013. 0.0000000001214. 0.00008043615. 0.0362116. 433 10417. 0.0042 10 318. 50,000,000,000 Glencoe/McGraw-Hill467Glencoe Algebra 1
NAME DATE8-3PERIODStudy Guide and Intervention(continued)Scientific NotationProducts and Quotients with Scientific NotationYou can use properties ofpowers to compute with numbers written in scientific notation.Example 1Evaluate (6.7 103)(2 10 5). Express the result in scientific andstandard notation.(6.7 103)(2 10 5) (6.7 2)(103 10 5) 13.4 10 2 (1.34 101) 10 2 1.34 (101 10 2) 1.34 10 1 or 0.134The solution is 1.34 10 1 or 0.134.Associative PropertyProduct of Powers13.4 1.34 101Associative PropertyProduct of Powers1.5088 1084.1 10Evaluate 5 . Express the result in scientific andExample 2standard notation. 1.5088 1.5088 108 4.1 1054.1105108Associative Property 0.368 103 (3.68 10 1) 103 3.68 (10 1 103) 3.68 102 or 368The solution is 3.68 102 or 368.Quotient of Powers0.368 3.68 10 1Associative PropertyProduct of PowersExercisesEvaluate. Express each result in scientific and standard notation.3 10 122 101.4 1042 102. 153. (3.2 10 2)(2.0 102)4. 121.2672 10 82.4 105. (7.7 105)(2.1 102)6. 107. (3.3 105)(1.5 10 4)8. 141. 23.3 10 121.1 109.72 1087.2 104 10 42.5 109. 210. FUEL CONSUMPTION North America burned 4.5 1016 BTU of petroleum in 1998.At this rate, how many BTU’s will be burned in 9 years? Source: The New York Times 2001 Almanac11. OIL PRODUCTION If the United States produced 6.25 109 barrels of crude oil in1998, and Canada produced 1.98 109 barrels, what is the quotient of their productionrates? Write a statement using this quotient. Source: The New York Times 2001 Almanac Glencoe/McGraw-Hill468Glencoe Algebra 1
NAME DATE8-3PERIODSkills PracticeScientific NotationExpress each number in standard notation.1. 4 1032. 2 1083. 3.2 1054. 3 10 65. 9 10 26. 4.7 10 7ASTRONOMY Express the number in each statement in standard notation.7. The diameter of Jupiter is 1.42984 105 kilometers.8. The surface density of the main ring around Jupiter is 5 10 6 grams per centimetersquared.9. The minimum distance from Mars to Earth is 5.45 107 kilometers.Express each number in scientific notation.11. 65,10012. 283,000,00013. 264,70114. 0.01915. 0.00000716. 0.00001003517. 264.918. 150 102Lesson 8-310. 41,000,000Evaluate. Express each result in scientific and standard notation.19. (3.1 107)(2 10 5)20. (5 10 2)(1.4 10 4)21. (3 103)(4.2 10 1)22. (3 10 2)(5.2 109)23. (2.4 102)(4 10 10)24. (1.5 10 4)(7 10 5)5.1 1061.5 1025. 2 Glencoe/McGraw-Hill7.2 10 54 1026. 3469Glencoe Algebra 1
NAME DATE8-3PERIODPracticeScientific NotationExpress each number in standard notation.1. 7.3 1072. 2.9 1033. 9.821 10124. 3.54 10 15. 7.3642 1046. 4.268 10 6PHYSICS Express the number in each statement in standard notation.7. An electron has a negative charge of 1.6 10 19 Coulomb.8. In the middle layer of the sun’s atmosphere, called the chromosphere, the temperatureaverages 2.78 104 degrees Celsius.Express each number in scientific notation.9. 915,600,000,00010. 638711. 845,32012. 0.0000000081413. 0.0000962114. 0.00315715. 30,62016. 0.000000000011217. 56 10718. 4740 10519. 0.076 10 320. 0.0057 103Evaluate. Express each result in scientific and standard notation.21. (5 10 2)(2.3 1012)22. (2.5 10 3)(6 1015)23. (3.9 103)(4.2 10 11)24. (4.6 10 4)(3.1 10 1)3.12 1031.56 1026. 81.82 1059.1 1029. 425. 328. 71.17 1025 106.72 1034.2 1027. 11.68 1048.4 1030. 22.015 10 33.1 1031. BIOLOGY A cubic millimeter of h
Glencoe/McGraw-Hill iv Glencoe Algebra 1 Teacher’s Guide to Using the Chapter 8 Resource Masters The Fast FileChapter Resource system allows you to conveniently file the resources you use most often. The Chapter 8 Resource Mastersincludes the core materials needed for Chapter 8. These material
