- •Study Skills Workshop
- •1.1 An Introduction to the Whole Numbers
- •1.2 Adding Whole Numbers
- •1.3 Subtracting Whole Numbers
- •1.4 Multiplying Whole Numbers
- •1.5 Dividing Whole Numbers
- •1.6 Problem Solving
- •1.7 Prime Factors and Exponents
- •1.8 The Least Common Multiple and the Greatest Common Factor
- •1.9 Order of Operations
- •THINK IT THROUGH Education Pays
- •2.1 An Introduction to the Integers
- •THINK IT THROUGH Credit Card Debt
- •2.2 Adding Integers
- •THINK IT THROUGH Cash Flow
- •2.3 Subtracting Integers
- •2.4 Multiplying Integers
- •2.5 Dividing Integers
- •2.6 Order of Operations and Estimation
- •Cumulative Review
- •3.1 An Introduction to Fractions
- •3.2 Multiplying Fractions
- •3.3 Dividing Fractions
- •3.4 Adding and Subtracting Fractions
- •THINK IT THROUGH Budgets
- •3.5 Multiplying and Dividing Mixed Numbers
- •3.6 Adding and Subtracting Mixed Numbers
- •THINK IT THROUGH
- •3.7 Order of Operations and Complex Fractions
- •Cumulative Review
- •4.1 An Introduction to Decimals
- •4.2 Adding and Subtracting Decimals
- •4.3 Multiplying Decimals
- •THINK IT THROUGH Overtime
- •4.4 Dividing Decimals
- •THINK IT THROUGH GPA
- •4.5 Fractions and Decimals
- •4.6 Square Roots
- •Cumulative Review
- •5.1 Ratios
- •5.2 Proportions
- •5.3 American Units of Measurement
- •5.4 Metric Units of Measurement
- •5.5 Converting between American and Metric Units
- •Cumulative Review
- •6.2 Solving Percent Problems Using Percent Equations and Proportions
- •6.3 Applications of Percent
- •6.4 Estimation with Percent
- •6.5 Interest
- •Cumulative Review
- •7.1 Reading Graphs and Tables
- •THINK IT THROUGH The Value of an Education
- •Cumulative Review
- •8.1 The Language of Algebra
- •8.2 Simplifying Algebraic Expressions
- •8.3 Solving Equations Using Properties of Equality
- •8.4 More about Solving Equations
- •8.5 Using Equations to Solve Application Problems
- •8.6 Multiplication Rules for Exponents
- •Cumulative Review
- •9.1 Basic Geometric Figures; Angles
- •9.2 Parallel and Perpendicular Lines
- •9.3 Triangles
- •9.4 The Pythagorean Theorem
- •9.5 Congruent Triangles and Similar Triangles
- •9.6 Quadrilaterals and Other Polygons
- •9.7 Perimeters and Areas of Polygons
- •THINK IT THROUGH Dorm Rooms
- •9.8 Circles
- •9.9 Volume
- •Cumulative Review
368 |
Chapter 4 Decimals |
THINK IT THROUGH GPA
“In considering all of the factors that are important to employers as they recruit students in colleges and universities nationwide, college major, grade point average, and work-related experience usually rise to the top of the list.”
Mary D. Feduccia, Ph.D., Career Services Director, Louisiana State University
A grade point average (GPA) is a weighted average based on the grades received and the number of units (credit hours) taken. A GPA for one semester (or term) is defined as
the quotient of the sum of the grade points earned for each class and the sum of the number of units taken. The number of grade points earned for a class is the product of the number of units assigned to the class and the value of the grade received in the class.
1.Use the table of grade values below to compute the GPA for the student whose semester grade report is shown. Round to the nearest hundredth.
Grade Value
A4
B3
C2
D1
F 0
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Geology |
4 |
C |
Algebra |
5 |
A |
Psychology |
3 |
C |
Spanish |
2 |
B |
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2.If you were enrolled in school last semester (or term), list the classes taken, units assigned, and grades received like those shown in the grade report above. Then calculate your GPA.
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5.2 |
2. 3.17 |
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14.24 6. 6,300 |
70 630 7 90 |
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7.213 |
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0.00107 |
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194,407 |
8. a. 6.62 b. |
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12. 2.747 million visitors |
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S E C T I O N 4.4 STUDY SET
VOCABULARY
Fill in the blanks.
1.In the division problem shown below, label the dividend, the divisor, and the quotient.
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2.To perform the division 2.7 9.45, we move the decimal point of the divisor so that it becomes the
number 27.
CONCEPTS
3.A decimal point is missing in each of the following quotients. Write a decimal point in the proper position.
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526 |
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21.04 |
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4.a. How many places to the right must we move the decimal point in 6.14 so that it becomes a whole number?
b.When the decimal point in 49.8 is moved three places to the right, what is the resulting number?
5.Move the decimal point in the divisor and the dividend the same number of places so that the divisor becomes a whole number. You do not have to find the quotient.
a.1.3 10.66
b.3.71 16.695
6.Fill in the blanks: To divide with a decimal divisor,
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the decimal point in the dividend and divide |
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7. To perform the division 7.8 14.562, the decimal points in the divisor and dividend are moved 1 place to the
right. This is equivalent to multiplying 14.562 by what
7.8
form of 1?
8.Use multiplication to check the following division. Is the result correct?
1.9170.9 2.13
9.When rounding a decimal to the hundredths column, to what other column must we look at first?
10.a. When 9.545 is divided by 10, is the answer smaller or larger than 9.545?
b.When 9.545 is divided by 0.1, is the answer smaller or larger than 9.545?
11.Fill in the blanks.
a.To find the quotient of a decimal and 10, 100, 1,000, and so on, move the decimal point to the
the same number of places as there are zeros in the power of 10.
b.To find the quotient of a decimal and 0.1, 0.01, 0.001, and so on, move the decimal point to the
the same number of decimal places as there are in the power of 10.
12.Determine whether the sign of each result is positive or negative. You do not have to find the quotient.
a.15.25 ( 0.5)
25.92
b.
3.2
NOTATION
13.Explain what the red arrows are illustrating in the division problem below.
467 3208.7
4.4 Dividing Decimals |
369 |
14.The division shown below is not finished. Why was the red 0 written after the 7 in the dividend?
2.3
2 4.70
4 0 7
6 1
GUIDED PRACTICE
Divide. Check the result. See Example 1.
15. |
12.6 6 |
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40.8 8 |
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Divide. Check the result. See Example 2. |
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98.21 23 |
20. |
190.96 28 |
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320.05 |
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125.12 |
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Divide. Check the result. See Example 3. |
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13.4 4 |
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24. |
38.3 5 |
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25. |
22.8 |
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28.5 |
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Divide. Check the result. See Example 4. |
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27. |
0.1932 |
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28. |
0.2436 |
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0.1131 |
30. |
0.1566 |
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Divide. Round the quotient to the nearest hundredth. Check the result. See Example 5.
11.83 |
16.43 |
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0.7 |
0.6 |
Estimate each quotient. See Example 6.
35.289.842 72.1
36.284.254 91.4
37.383.76 7.8
38.348.84 5.7
39.3,883.284 48.12
40.5,556.521 67.89
41.6.1 15,819.74
42.9.2 19,460.76
Find each quotient. See Example 7. |
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43. |
451.78 100 |
44. |
991.02 100 |
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45. |
30.09 |
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27.07 |
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47. |
1.25 0.1 |
48. |
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545.2 |
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67.4 |
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0.001 |
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0.001 |
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370 |
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Chapter 4 |
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Decimals |
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Divide. See Example 8. |
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51. |
110.336 12.8 |
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52. |
121.584 14.9 |
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53. |
91.304 ( 22.6) |
54. |
66.126 ( 32.1) |
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55. |
20.3257 |
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56. |
48.8933 |
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0.001 |
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57. |
0.003 ( 100) |
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0.008 ( 100) |
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Evaluate each expression. See Example 9. |
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59. |
2(0.614) 2.3854 |
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2(1.242) 0.8932 |
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0.2 0.9 |
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61. |
5.409 3(1.8) |
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62. |
1.674 5(0.222) |
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64. |
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65. |
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66. |
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nearest hundredth.)
TRY IT YOURSELF
Perform the indicated operations. Round the result to the specified decimal place, when indicated.
67. |
4.5 |
11.97 |
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4.1 |
14.637 |
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69. |
75.04 |
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70. |
22.32 |
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71. |
0.036 |
72. |
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73. |
2.889 |
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75. |
3(0.2) 2(3.3) |
76. |
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30(0.4)2 |
2(0.2) 0.5 |
77.Divide 1.2202 by 0.01.
78.Divide 0.4531 by 0.001.
79.5.714 2.4 (nearest tenth)
80.21.21 3.8 (nearest tenth)
81. |
39 ( 4) |
82. |
26 ( 8) |
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83. |
7.8915 .00001 |
84. |
23.025 0.0001 |
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86. |
0.0092 |
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0.017 |
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87.12.243 0.9 (nearest hundredth)
88.13.441 0.6 (nearest hundredth)
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89. |
1,000 |
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90. |
10,000 678.9 |
91. |
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94. Divide 1.2 by 0.64 |
APPLICATIONS
95.BUTCHER SHOPS A meat slicer trims 0.05-inch- thick pieces from a sausage. If the sausage is 14 inches long, how many slices are there in one sausage?
96. ELECTRONICS The volume control |
VOLUME |
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on a computer is shown to the right. If |
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the distance between the Low and High |
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equally spaced volume settings? |
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97.COMPUTERS A computer can do an arithmetic calculation in 0.00003 second. How many of these calculations could it do in 60 seconds?
98. THE LOTTERY In December of High 2008, fifteen city employees of Piqua,
Ohio, who had played the Mega Millions Lottery as a group, won the jackpot. They were awarded a total of $94.5 million. If the money was split equally, how much did each person receive?
(Source: pal-item.com)
99.SPRAY BOTTLES Each squeeze of the trigger of a spray bottle emits 0.017 ounce of liquid. How many squeezes are there in an 8.5-ounce bottle?
100.CAR LOANS See the loan statement below. How many more monthly payments must be made to pay off the loan?
American Finance Company |
June |
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Paid to date: $547.30 |
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payment: |
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$42.10 |
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Loan balance: $631.50 |
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101.HIKING Refer to the illustration below to determine how long it will take the person shown to complete the hike. Then determine at what time of the day she will complete the hike.
Departure
Arrival
A.M.
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The hiker walks |
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2.5 miles |
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7 |
6 |
5 |
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each hour. |
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Start |
27.5-mile hike |
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102.HOURLY PAY The graph below shows the average hours worked and the average weekly earnings of U.S. production workers in manufacturing for the years 1998 and 2008. What did the average production worker in manufacturing earn per hour
a. in 1998? |
b. in 2008? |
U.S. Production Workers in Manufacturing
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800 |
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700 |
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$710.70 |
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weekly earnings ($) |
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$556.83 |
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500 |
41.4 hr |
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2008 |
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Source: U.S. Department of Labor Statistic
103.TRAVEL The illustration shows the annual number of person-trips of 50 miles or more (one way) for the years 2002–2007, as estimated by the Travel Industry Association of America. Find the average number of trips per year for this period of time.
U.S. Domestic Leisure Travel (in millions of person-trips of 50 mi or more, one way)
1,600 |
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1,500 |
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1,482.5 |
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1,400 |
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1,300 |
1,388.2 |
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1,200 |
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2007 |
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Source: U.S. Travel Association
104.OIL WELLS Geologists have mapped out the types of soil through which engineers must drill to reach an oil deposit. See the illustration below.
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Silt |
0.68 mi |
Rock |
0.36 mi |
Sand |
0.44 mi |
Oil |
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4.4 Dividing Decimals |
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a.How far below the surface is the oil deposit?
b.What is the average depth that must be drilled each week if the drilling is to be a four-week project?
105.REFLEXES An online reaction time test is shown below. When the stop light changes from red to green, the participant is to immediately click on the large green button. The program then displays the participant’s reaction time in the table. After the participant takes the test five times, the average reaction time is found. Determine the average reaction time for the results shown
below.
Test |
Reaction Time |
The stoplight |
The button |
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to watch. |
to click. |
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0.219 |
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0.233 |
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0.204 |
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here |
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on |
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0.297 |
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green |
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0.202 |
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AVG. |
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106.INDY 500 Driver Scott Dixon, of New Zealand, had the fastest average qualifying speed for the 2008 Indianapolis 500-mile race. This earned him the pole position to begin the race. The speeds for each of his four qualifying laps are shown below. What was his average qualifying speed?
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Lap 1: 226.598 mph |
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Lap 2: 226.505 mph |
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Lap 3: 226.303 mph |
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Lap 4: 226.058 mph |
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(Source: indianapolismotorspeedway.com) |
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WRITING
107.Explain the process used to divide two numbers when both the divisor and the dividend are decimals. Give an example.
108.Explain why we must sometimes use rounding when we write the answer to a division problem.
109.The division 0.5 2.005 is equivalent to 5 20.05 . Explain what equivalent means in this case.
110.In 3 0.7, why can additional zeros be placed to the right of 0.7 without affecting the result?
111.Explain how to estimate the following quotient: 0.75 2.415