Selected Solutions Solutions are included for: Even-Numbered Chapter Review Exercises All Concepts Analysis Exercises Even-Numbered Practice Test Exercises Even-Numbered Cumulative Practice Test Exercises Other solutions are included in the Student Solutions Manual Odd-Numbered Chapter Review Exercises Odd-Numbered Practice Test Exercises Odd-Numbered Cumulative Practice Test Exercises 163 Copyright © 2014 Pearson Education, Inc Copyright © 2014 Pearson Education, Inc Chapter One Review of Basic Concepts fCHAPTER REVIEW EXERCISES (a) (b) (c) 75 = 0.075 1,000 Since the denominator is 1,000, the last digit of the numerator is in the thousandths place 21 = 2.1 10 Since the denominator is 10, the last digit of the numerator is in the tenths place 652 = 0.00652 100,000 Since the denominator is 100,000, the last digit of the numerator is in the hundredthousandths place (a) (c) (e) 98 The rounded answer is 100 ,786 The rounded answer is 26,000 93 The rounded answer is smaller: 0.83 0.825 n n Compare each place value, left to right, until two digits in the same place value are different, and compare those digits 0.83 > 0.825 (b) (d) (f) 94 The rounded answer is 90 0.0 36 The rounded answer is 0.07 876 The rounded answer is 0.825 is smaller larger: 4.831 4.820 n n 4.831 > 4.820 4.831 is larger 10 smaller: 1.023 1.03 n n 1.023 < 1.03 The 1.023 in part is smaller and has been machined more 165 Copyright © 2014 Pearson Education, Inc 166 CHAPTER 1: REVIEW OF BASIC CONCEPTS 12 (a) 6.2 + 32.7 + 46.82 + 0.29 + 4.237 221 6.200 32.700 46.820 0.290 4.237 90.247 (b) 86.3 + 9.2 + 70.02 + + 2.7 The decimal point in a whole number is at the end 121 86.30 9.20 70.02 3.00 2.70 + 171.22 32 14 12 Estimate 60 70 + 200 330 16 (a) (c) 18 20 Estimate 12,300 4,500 7,800 Estimate 6,800 500 6,300 Exact 1 57.32 74.26 + 174.85 $ 306.43 Exact 12,346.87 4, 468.63 7,878.24 Exact 6, 767 478 6, 289 (b) (d) Estimate 3,500 3,100 400 Estimate 300 100 200 9 10 100.00 75 + 25 12.75 87.5 100 The family cleared $87.25 on the two items sold A=EB A = 4.86 in 1.972 in A = 2.888 in 22 C = D E C = 3.7 in 1.6 in C = 2.1 in Copyright © 2014 Pearson Education, Inc Exact 3, 495 3,090 405 Exact 293.86 148.00 145.86 COLLEGE MATHEMATICS 24 167 6(3)(2)(4) = 18(2)(4) = 36(4) = 144 18 u 36 28 36 u 144 236 u 244 11 944 944 472 57584 , 30 26 327 39 u 943 81 12, 753 The bookstore received $12,753 for the books 32 $ 112 u 105 560 11 $11, 760 The dealer took in $11,760 on the sale Estimate 30 u 40 1200 Exact $ 33.25 u 37 232 75 997 $1, 230.25 The sound system installer was paid $1,230.25 Estimate 34 A luw 200 u 100 20,000 Exact A luw 234.6 u 123.2 28,902.72 Check 234.6 u 123.2 123.2 u 234.6 4 2 70 692 23 46 73 92 492 696 24 64 28,902.72 28,902.72 The area of the field is 28,903 ft2 36 12 12 26 178.6 u 0.28 u 111 664 178.6 u 0.2 11 14 28 35 72 50.008 u 250.040 or 250.04 50.00 The employee earns $250.04 Copyright © 2014 Pearson Education, Inc 168 CHAPTER 1: REVIEW OF BASIC CONCEPTS 38 29.25 y 0.36 81R9 0.36 29.25 288 45 36 44 56 y The band will have members in each row 46 average, nearest cent (hundredth) 72.252| $72.25 $72.25 72.252 223 $ 74.98 20 361.260 361.260 35 23.72 35 51.27 1111 125.36 1010 + 85.93 212 010 $ 361.26 2626 2525 1210 1010 48 (a) (b) (c) 50 52 54 56 40 364.8 y 60.8 364.8 36 48 48 10,160 y 20 508 20 10,160 100 16 160 160 base o 56 m exponent 56 = u u u u u = 15,625 base o 1.22 m exponent 1.22 = 1.2 u 1.2 = 1.44 base o 106 m exponent 106 = 1,000,000 (a) 2,500 = 50 since 50 u 50 = 2,500 (b) 1.44 = 1.2 since 1.2 u 1.2 = 1.44 (c) 289 = 17 since 17 u 17 = 289 (d) 81 = since u = 81 (a) (d) 42 calculator options: 81 u 100 = 300 u 100 = 500 75 u 10,000 = 750,000 40.6 u 10 = 406 2+33y3= 2+9y3= 2+3= 18 y 33 (b) (e) Multiply Divide Add Divide Subtract Copyright © 2014 Pearson Education, Inc (c) 2.2 u 1,000 = 2,200 Copyright © 2014 Pearson Education, Inc Copyright © 2014 Pearson Education, Inc COLLEGE MATHEMATICS 171 92 A = bh A = 16.2(14.2) A = 230.04 in2 94 A = lw A = 15.9(12.7) A = 201.93 cm2 96 2.5 ft A = s2 A = 2.5 A = 6.25 ft2 2.5 ft 98 A = lw A = 25(8) A = 200 ft2 A2 walls = 2(200) = 400 ft 100 Adoorway Afront lw 7(6) 42 ft lw 20(12) 240 ft Abrick 198 ft 240 42 198 ft bricks = 1,188 bricks ft Chapter Concepts Analysis 1.2 + n = 1.7 n = 1.7 1.2 n = 0.5 (3 1) z (7 3) 72z41 5z3 Answers may vary u n = 4.5 n = 4.5 y n = 0.9 n =6 n = 62 n = 36 y 12 z 12 y z2 Answers may vary Perform operations within parentheses (or other grouping symbols) beginning with the innermost set of parentheses Evaluate exponential operations and find square roots in order from left to right Multiply and divide in order from left to right Add and subtract in order from left to right Copyright © 2014 Pearson Education, Inc 172 CHAPTER 1: REVIEW OF BASIC CONCEPTS 2.5 + 4.9 = The order of operations states that multiplication must be done before addition 9 2.5 + 4.9 7.4 81 + = 14 Write in the WHQWKV column and carry the to the XQLWV column 1+2+4=7 Wrong because 92 81 Find ?2 = to get On some calculators: + 5(4) = + 20 = 22 Correct 10 Addition requires the decimals to be in a vertical line, so similar place values are added, just as with whole numbers 11 No, perfect squares have an even number of decimal places 12 Yes, the number of decimal places in a perfect cube is a multiple of three, and is a perfect cube 13 No, any decimal multiplied times itself will have twice as many decimal places (0.12 = 0.01, 0.112 = 0.0121, 0.1112 = 0.012321, etc.) Chapter Practice Test nearest hundredth 12 11 12 $ 61,532 47,245 $ 14,287 4.0 4.0 (rounded up since is five or more) $2,133.33 12 25, 600.00 24 16 12 40 36 40 36 40 36 40 36 Copyright © 2014 Pearson Education, Inc nearest cent (hundredths) 10 46 u 103 $4 $4.83 (rounded down since is less than 5) 46, 000 COLLEGE MATHEMATICS 12 173 53 (3 2) u Do operation within parentheses first Evaluate exponentiation and square root from left to right Multiply Subtract 5u 125 u 125 15 110 14 16 Estimate: Exact: $335 00 u 45 u 50 $ 15, 000 675 13 40 $15, 075 17 u 34 The professor should give 34 points to the student The total cost is $15,075 18 1.11 25 27.75 25 27 25 25 25 20 52.38 y 10,000 = 0052.38 = 0.005238 24 1.485 1.485 0.010 0.010 1.475 1.495 The limit dimensions of the part are 1.475 in to 1.495 in 55 33 26 7.96 u 16 11 47 76 79 127.36 The length of steel required is 127.36 ft 28 l = 18.5 ft w = 2.5 ft P = 2l + 2w P = 2(18.5 ft) + 2(2.5 ft) P = 37 ft + ft P = 42 ft A = lw A = 18.5 ft(2.5 ft) A = 46.25 ft2 Copyright © 2014 Pearson Education, Inc 22 Estimate, nearest whole number 3.85 + 7.46 +7 11 ... with the innermost set of parentheses Evaluate exponential operations and find square roots in order from left to right Multiply and divide in order from left to right Add and subtract in order... numbers 11 No, perfect squares have an even number of decimal places 12 Yes, the number of decimal places in a perfect cube is a multiple of three, and is a perfect cube 13 No, any decimal multiplied... Chapter One Review of Basic Concepts fCHAPTER REVIEW EXERCISES (a) (b) (c) 75 = 0.075 1,000 Since the denominator is 1,000, the last digit of the numerator is in the thousandths place 21 = 2.1