Chapter 3€¦ · · 2009-11-05C. Units made up of base units are derived units D. SI details in...

Copyright © 2004 Brooks/Cole, a division of Thomson Learning, Inc.No part of this work may be reproduced without the written permission of the publisher.

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Free Study Guide forCracolice • Peters

Introductory Chemistry: An Active Learning ApproachSecond Edition

www.brookscole.com/chemistry

Chapter 3Measurement and

Chemical Calculations

Chapter 3–Assignment A: Exponential Numbers

Chemists describe the universe, which means that we need to use very large and very smallnumbers. Exponential notation is simply the easiest way to write these numbers. It's easierthan you might think, because having ten fingers and ten toes, we're decimal-basedcreatures.

Don't overlook the importance of this assignment just because your calculator can doexponential numbers. Historically, many math errors ("decimal slippage") in this chapterand the chapters to follow occur because students enter exponential numbers intocalculators incorrectly, and cannot tell they have made a mistake.

Section 3.2 introduces an important method of learning problem solving skills, by solvingexample problems. There are opaque shields in your text. Using a shield correctly, asdirected in the text, is the best way to learn to solve problems in this course. Using theshield incorrectly is a quick path to trouble. Try to do the examples with the shield in place,so you can't peek at the answers, and you must work the problem yourself. Remember, youmust later work the exam problems yourself. Look for the big ideas....

1) Any decimal number can be written in exponential notation. Exponential notationexpresses a number as a coefficient C (between 0 and 9) multiplied by 10 raised tothe e power, in general, C!¥!10e. When e is larger than 0, 10e is larger than 1; when eis smaller than 0, 10e is smaller than 1. (Remember that 100 = 1.)

2) To add, subtract, multiply, or divide numbers in exponential notation, following theinstructions that are appropriate for your calculator.

Learning Procedures

Study Sections 3.1–3.2. Focus on Goals 1–2 as you study.

Strategy Begin the study of a new chapter with a brief preview. For each section, lookat its title; glance quickly at the Goals; scan the text for terms given inboldface. Look at the illustrations and tables. Make a mental note of allprocedures and summaries; they can shorten your chapter outline. TheChapter in Review Section lets you check your preview at a glance.

Chapter 3 Measurement and Chemical Calculations


9

Write an outline as you study this assignment. Don't use a highlighter. Inthis chapter and in Chapter 2, we “write” an outline along with you. Thisoutline appears at the end of each study guide assignment. Note: Ouroutline is a suggestion, not a statement of what your outline should be. Yourwords are better because they express your way of thinking about the topic;but your words and ours should express the same idea.

Keep your outline informal. Begin with the chapter letter and title. Usetextbook section numbers instead of I, II, III, and so on for your mainheadings. Page references help the outline. Be brief, but not so brief that youmust check the text to find out what the entry means.

Answer Questions, Exercises, and Problems 1–6. Check your answers with those atthe end of the chapter.

Workbook If your instructor recommends the Active Learning Workbook, doQuestions, Exercises, and Problems 1–6.

Chapter 3–Assignment A Suggested Outline

3.1 Introduction to MeasurementA. SI units are metric unitsB. Seven base units, including mass, length, time, and temperatureC. Units made up of base units are derived unitsD. SI details in Appendix II

3.2 Exponential (Scientific) NotationA. Standard form: C ¥ 10e. C is coefficient; e is exponent.B. See Procedure for writing numbers in exponential notation, textbook page 48

1. Write coefficient with decimal after first nonzero digit. Follow with "¥ 10"2. Exponent is number of places decimal moved.3. If coefficient is smaller than number (C < n), exponent is larger than 0 (e > 0,

a positive number); if coefficient is larger (C > n), exponent is smaller than 0(e < 0, a negative number).

C. To change from exponential notation to decimal form, perform multiplication.Positive exponent means large number, so decimal moves right same number ofplaces as exponent. Negative exponent, small number, move decimal left.

D. How to use calculator for multiplication with exponential notation, textbook page 50.

Chapter 3–Assignment B: Dimensional Analysis

Dimensional analysis is the easiest way to solve many problems in this chemistry courseand in those that follow. Your text uses dimensional analysis whenever applicable. The onlymathematical operations required are multiplication and division. When to multiply andwhen to divide are determined by logical thinking, and the use of measurement units letsyou check the correctness of your setup.

Study Guide for Introductory Chemistry: An Active Learning Approach


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The guiding principle of dimensional analysis is that the dimensions on each side of a PERexpression must match. To solve a problem by dimensional analysis you do the followingthings:

1) Identify the GIVEN quantity, including units.

2) Identify the units of the WANTED quantity.

3) Write out the PER/PATH.

4) Write the calculation setup, including units.

5) Calculate the answer.

6) Check to be sure the numerical answer and its associated units make sense.

The most important skill in dimensional analysis is arriving at the proper setup of theproblem, including units. Use reason, logic, and your mathematical skills to arrive at thesesetups. Don't find the setups by just juggling units. Try to grasp the logic of the problem.

Learning Procedures

Study Section 3.3. Focus on Goal 3 as you study.

Strategy Continue outlining the chapter, focusing on bold-faced terms and on thesummaries that appear in the chapter. Our suggested outline appears at theend of this assignment.

Answer Questions, Exercises, and Problems 7–11. Check your answers with those atthe end of the chapter.


Chapter 3–Assignment B Suggested Outline

3.3 Dimensional AnalysisA. PER expressions

1. 7 days per week, 7 days/week, and 7 days = 1 week all have the same meaning.

2. PER expressions can be used when two quantities are directly proportional to each other.

B. PER, PATH, GIVEN, WANTED1. Every PER expression can be written in two ways, as two fractions that are

reciprocals of each other.2. PATH is a unit path, a series of steps from the units of the given quantity

(GIVEN) to the wanted quantity (WANTED). Written as GIVEN Æ WANTEDthrough as many steps are needed. Conversion factor must be known foreach step.

C. Calculations1. Start with GIVEN quantity.2. Multiply by conversion factors in unit path.3. Include units in all setups.



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4. If setup yields “nonsense units”—units that don't make sense—the setup and answer are wrong.

5. Be sure numerical answer makes sense. Use larger/smaller reasoning when possible.

6. To divide by a fraction, multiply by its inverse; “invert and multiply.”7. When there are two or more steps, do not calculate intermediate answers

unless required.D. See Procedure for dimensional analysis, textbook page 58

Chapter 3–Assignment C: Mass, Weight, and Metric Units

Chapter 3–Assignment A got you used to thinking in exponential notation, based on thedecimal system. The metric system also uses the decimal system to convert betweenmeasurements of mass, length, and volume.

1) The mass of an object does not change in different gravitational fields; the weightof that object does change.

2) The metric system of measurement identifies a unit, and then expresses larger orsmaller quantities as multiples or submultiples of 10 times that unit. These multiplesor submultiples are known by prefixes that may be applied to any measurement unit.

3) The SI metric unit of mass is the kilogram, kg. In the laboratory, massmeasurements are commonly expressed in grams, g, or milligrams, mg.

4) The metric unit of length is the meter, m.

5) The SI unit of volume is the cubic meter. The more common unit in chemistry is thecubic centimeter, cm3. Volumes of liquids and gases are most often expressed inliters, L, or milliliters, mL.

6) The important metric prefixes for this course are kilo- (1000), centi- (0.01) andmilli- (0.001).

7) By definition, 1 mL ≡ 1 cm3.

8) Because the metric system is decimal based, conversions between larger and smallermetric units involve simply moving the decimal point.

Learning Procedures

Study Section 3.4. Focus on Goals 4–8 as you study.


Answer Questions, Exercises, and Problems 12–20. Check your answers with thoseat the end of the chapter.



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Chapter 3–Assignment C Suggested Outline

3.4 Metric UnitsA. Mass

1. Weight measures gravitational attraction; mass measures amount of matter.Weight depends on where in universe object is; mass always the sameanywhere.

2. Kilogram, kg, is official mass unit, about 2.2 pounds. Gram, g, more common

3. Memorize prefixes and symbols: kilo-, k, 1000; centi-, c, 1/100 or 0.01; milli-, m, 1/1000 or 0.001. Others in Table 3.2, textbook page 3.12.

4. Combine metric symbol with unit abbreviation, as kg = kilogram, cg = centigram, mg = milligram

B. Length1. Base unit is meter—3 inches more than 1 yard2. Kilometer, 0.6 mile; centimeter, width of a fingernail;

millimeter, thickness of a dimeC. Volume

1. Cubic meter, m3, a derived unit (a combination of base units)2. Cubic centimeter, cm3, more common3. Liquid volume: liter (L) and milliliter (mL)4. 1 mL = 1 cm3

D. Metric conversions1. Use dimensional analysis to convert metric units.2. Most metric conversions completed by moving the decimal point.3. Use larger/smaller rule to be sure decimal moved in correct direction.

Chapter 3–Assignment D: Significant Figures

We use two kinds of numbers: exact and approximate. Exact numbers are correct as given.They contain no error, or uncertainty. Examples of these are counting numbers, as howmany times you repeat a laboratory procedure, or defined numbers, as the number ofcentimeters in a meter.

Scientific data are obtained from experiments. These data come from measurements madeby reading a scale on a balance, a thermometer, a graduated cylinder, or some other device.Measurements are never exact; they involve both imperfect human judgment and imperfectmeasuring instruments. Measurements are subject to uncertainty, and the best ofmeasurements can always be improved.

The main ideas in this assignment are:

1) Significant figures are used to express the size of the uncertainty in measurementsand in calculations derived from measurements.

2) The number of significant figures in a measurement is the number of digits that areknown accurately plus one digit that is uncertain.



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3) If a quantity is properly expressed, the uncertain digit is the last digit shown.

4) To count the number of significant figures in a measurement, start with the firstnonzero digit on the left and end with the uncertain digit, the last digit shown on theright.

5) To round off a number to the proper number of significant figures, leave theuncertain digit unchanged if the digit to its right is less than 5. Increase the uncertaindigit by one if the digit to its right is 5 or more.

6) In addition and subtraction, round off a sum or difference to the first column thathas a uncertain digit.

7) In multiplication and division, round off a product or quotient to the same number ofsignificant figures as the smallest number of significant figures in any factor.

8) In chain calculations, keep intermediate answers in your calculator and round offonly the final answer.

Learning Procedures

Study Section 3.5. Focus on Goals 9–12 as you study.



Workbook If your instructor recommends the Active Learning Workbook, doQuestions, Exercises, and Problem 21–26.

Chapter 3–Assignment D Suggested Outline

3.5 Significant FiguresA. See caption to Figure 3.5, textbook page 64. Uncertainty is the ± value of a

measurement. The “uncertain digit” is the digit value in which the uncertaintyappears, such as hundreds, units, tenths, and so on.

B. Significant figures (sig figs) ≡ number of digits in a quantity that are known for sure plus 1, the uncertain digit.

C. Uncertain digit is last digit written.D. Counting sig figs: Begin with first nonzero digit, end with uncertain digit, the

last digit shown.E. Location of decimal point has nothing to do with sig figs.F. In very small numbers, zero between decimal point and first nonzero digit are

not significant. Begin counting at first nonzero digit, not at decimal point.G. In very large numbers, zeros before decimal point usually are not significant.

Write large numbers in exponential notation (exno) to put uncertain digit to rightof decimal point.

H. Zeros to locate decimal are never significant.



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I. If uncertain digit is a zero to right of decimal, it must be written. Uncertain digitmust be the last digit shown. If uncertain digit is a zero, use exno if necessary toput it to right of decimal.

J. Counting numbers and numbers fixed by definitions are exact. They have no uncertainty. They are infinitely significant.

K. Summary of sig figs on textbook page 65.L. Rules for rounding off

1. If the first digit to be dropped is less than 5, leave the digit before it unchanged

2. If the first digit to be dropped is 5 or more, increase the digit before it by 1M. Sig fig rule for addition and subtraction: Round off to first column with a

uncertain digit.N. Sig fig rule for multiplication and division: Answer has same number of sig figs

as the smallest number of sig figs in any factor.

Chapter 3–Assignment E: To and from the Metric System, Temperature,Proportionality, and Density

Now that you have become familiar with dimensional analysis, the metric system, andsignificant figures, you are ready to use these tools in calculations involving measurements.

You will use metric measurements in your study of chemistry. In this assignment only willyou be concerned with United States Customary System units, and then just to make a fewconversions between them and the metric units.

In the laboratory, temperature measurements are expressed in Celsius degrees, °C. BecauseCelsius degrees and the familiar Fahrenheit degrees, °F, do not have the same zero point,you cannot use dimensional analysis to convert from one to the other. You must make thisconversion by algebra, using the equation T°F – 32 = 1.8 T°C or some similar equation. Thekelvin temperature scale also does not share a zero point with the Celsius scale, soconversions between the two scales must also be done algebraically using TK = T°C +273.15. Most other calculations in this course can be done using dimensional analysis.

Density is a useful physical property that is a combination of the base units mass and(length)3, which is volume. Because density is an intrinsic property—not dependent on thesize of the sample—it has many uses. For example, canned peas are graded by density; thehigher the density, the older and presumable tougher the pea. The peas are placed into tanksof salt water solutions of different densities, and the younger peas float and the older peassink.

Look for these big ideas:

1) The Fahrenheit and Celsius temperature scales are related by the equationT°F – 32 = 1.8 T°C.

2) The kelvin and Celsius temperature scales are related by the equation TK =T°C + 273.15. Note that there is no degree sign before the kelvin temperature.

3) The defining equation for density is: density ≡

†

massvolume



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4) Because the defining equation for density is a PER expression, density problemsmay be solved by either dimensional analysis or algebra.

Learning Procedures

Study Sections 3.6–3.8. Focus on Goals 13–20 as you study.




Chapter 3–Assignment E Suggested Outline

3.6 Metric–USCS ConversionsA. See Table 3.3, textbook page 71

3.7 TemperatureA. Three scales, Celsius, Fahrenheit, kelvin

1. T°F – 32 = 1.8 T°C2. TK = T°C + 273.153. Degree sign not used for kelvins

B. Temperature conversions done by algebra1. First solve equation algebraically for the unknown.2. Then substitute given values and calculate answer.

3.8 Proportionality and DensityA. When two quantities change at the same rate, the are directly proportional to one

anotherB. Density ≡ mass per unit volume. ≡ means “is defined as”C. Word definition can be written as a defining equation:

density ≡

†

massvolume

D ≡

†

mV

D. Units set by definition and defining equation: mass units over volume units. Examples: kg/m3, g/cm3, g/mL, g/L.

Chapter 3–Assignment F: Summary and Review

Let's start with calculators. We assume you have one. You don't need an expensive one, butit should be able to display exponential notation and logarithms. A $10 calculator will getyou through this course and the chemistry courses that follow. If you do have a calculator,do you know where its instruction book is? Go find it. Your calculator can do much moreand make your life much easier than it is now, if you let it. (More about this later.) Start



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with the section on chain calculations; to find this section, look up “chain calculations” or“parentheses” in the instruction book's index. If there are no such sections or if yourcalculator's instruction book is long gone, study well the section on chain calculations inAppendix I. The important thing is to leave the intermediate answers in the calculator andwrite down only the final answer. Your time is valuable; let the calculator remember theintermediates.

This is an important chapter, because measurement is a major part of what science andengineering are all about. Let's review the highlights of Chapter 3 to see how theassignments lead smoothly from one to the other.

Exponential notation and the metric system go together, because they are both based onpowers of ten. There is a very real human tendency to size our measurement units such thatall measurements have values ideally between 1 and 1000 (even better, between 1 and 10).Exponential notation and the metric system let us do that easily. Getting your calculator intoexponential notation is simple, if you know what key turns on the exponents. It's markedEE, EEX, or EXP. Look for it, then use it with the +/– key to learn how to enter negativeexponents with positive coefficients and vice versa. Do it now.

You may have trouble moving the decimal point in the wrong direction when convertingfrom one metric unit to another. You are not likely to make this mistake if you set up theproblem, at least in your mind, using dimensional analysis. Remember that there are morelittle units in a given measurement than big units—more centimeters, for example, thanmeters. Test all your answers mentally to see that they meet this logical requirement.

Dimensional analysis is a powerful problem solving method that you can use in many fieldsother than chemistry. (Try it on word problems in algebra class.) You may have somedifficulty with dimensional analysis at first. For almost all people this difficulty disappearsin a week or so. At the end of a month, they are such confirmed “dimensionalanalysists”they wonder why anyone would solve a problem using any other method. If the procedureseems awkward, keep working with it for a couple of weeks until you master it; don't judgedimensional analysis until you see its full merits.

Your main difficulty is likely to be identifying the given quantity. You must develop thisskill carefully, as you will use it continually. Usually, the given quantity is the only value inthe question that is not a PER expression. Once you have the given quantity, you select yoursetups in problem solving so you have something logical and meaningful at the end of eachstep. You will do this automatically if you think your way through the problem, rather thansimply plugging in and canceling units.

Significant figures can be a major problem for some students. The digit that gives the mosttrouble is zero. (What your test score may be if you don't learn significant figurescorrectly.) Leading zeros, on the far left of a number, are never significant. Trailing zeros,on the far right of a number, may or may not be significant. Trailing zeros to the right of thedecimal point are always significant, while trailing zeros to the left of the decimal point areprobably not significant. When in doubt, put the number in exponential notation, then countthe digits. Be very careful when adding or subtracting in a chain calculation.

Using a calculator that spews out digits until the display is full makes the “sig fig”problem worse. Don't regard calculator answers as correct. They are not! They are correctto the proper number of significant figures, and no more. Life gets much easier here if youknow where your calculator's instruction book is.



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When a calculator is set to display a fixed number of decimal places, it will round correctlyto that number. However, the calculator in this instance will not always display the correctnumber of significant figures. You must check your calculator, then adjust its display ifneeded. In exponential notation, the number of significant figures stays constant (as you setit) and the decimal point “floats.”

Significant figures are best learned by using them continuously, even outside the laboratory.Use them whenever you make a measurement, even when you alone must approve yourwork.

After learning to express mass and volume units correctly, we combined these quantities toobtain density. Density problems are easily solved using either algebra or dimensionalanalysis. The only trick to remember when solving density or volume problems is that1!mL!= 1 cm3.

If solving area, (length)2, or volume, (length)2, problems is confusing, remember that theentire conversion factor, not just the unit, must be raised to the power. Try this experiment.Draw a square 1 dm (10 cm) on a side. Now draw a square 1 cm on a side. Cut out thesmaller square, put it on the larger square, and estimate how many small squares you wouldneed to cover the larger square completely. You can see that although 10 cm = 1 dm,102!cm2 = 100 cm2 = 12 dm2.

Although there are no Goals in Section 3.9, don't overlook this section. Figure 3.9 is a one-page summary of this chapter. Finally, you get to the end of this course the same way youget to Carnegie Hall.... Thoughtful and reflective practice, to quote the title of Section 3.10.There is no substitute for working lots of problems without looking at our solution untilyou’ve completed the entire solution for yourself. When you make a mistake, reflect on theerror in your procedure and think about why it was wrong. Making mistakes while doinghomework is an excellent way to learn! Students who make a learning experience out ofmistakes while practicing homework problems rarely repeat those mistakes on exams.

Learning Procedures

Study Sections 3.9–3.10.

Review your lecture and textbook notes.

the Chapter in Review and the Key Terms and Concepts, and read the StudyHints and Pitfalls to Avoid.

Answer Concept-Linking Exercises 1–5. Check your answers with those at the endof the chapter.

Questions, Exercises, and Problems 47–51. Include Questions 52–55 ifassigned by your instructor. Check your answers with those at the end of thechapter.

Workbook If your instructor recommends the Active Learning Workbook, doQuestions, Exercises, and Problems 47–48. Include Questions 49–52 ifassigned by your instructor.



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Take the chapter summary test that follows. Check your answers with those at theend of this assignment.

Chapter 3 Sample Test

1) Where decimal numbers are given, write exponential numbers; where exponentialnumbers are given, write their decimal equivalents.

413,400 6.91 ¥ 107

0.00103 1.47 ¥ 10– 4

2) Perform the following operations; leave 3 digits in your answers.

4.1 ¥ 10– 6 + 1.59 ¥ 10– 5 = 6.7 ¥ 103 + 2.61 ¥ 104 =

7.14 ¥ 103 – 3.9 ¥ 102 = 8.34 ¥ 10– 1 – 3.6 ¥ 10– 2 =

3) Perform the following operations; leave 3 digits in your answers.

(1.16 ¥ 10– 3)(6.32 ¥ 10–11) = (4.62 ¥ 10– 6)(2.17 ¥ 108) =

†

(9.76 ¥ 107)(8.17 ¥ 103)(1.23 ¥ 101)

=

†

4.39 ¥ 104

(107)(7.11 ¥ 101) =

4) The Lagrange points are points in space between the earth and moon; at these pointsthe gravity of the earth exactly cancels the gravity of the moon. What would be themass and the weight of a 70 kg person at one of these points? (1 kg = 2.20 lb)

5) How many significant figures are in the measured quantity 0.099 gram?

6) Round off 2.6034 kilometers to three significant figures.

7) Express the following sum to the correct number of significant figures. All numbersrepresent measured quantities.

16.08 + 0.043 + 121.80 + 7.99463 =



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8) Express the following to the correct number of significant figures. All numbers arefrom measurements.

2.193 ¥

†

5.8764.88

¥

†

0.06564.06

=

Questions 9–14: A correct setup, beginning with the given quantity, is required for acorrect answer.

9) How many dollars can you earn in a part-time job in three months if your hourlywage is $6.45, you average 13.6 hours per week, and there are 4.33 weeks in amonth?

10) If 2.54 cm ≡ 1 inch, how many centimeters are in 45.0 inches?

11) How many millimeters are in 40.1 meters?

12) Convert 9.45 kilometers to meters.

13) State the number of quarts in 3440 cm3, if 1 liter = 1.06 quart.



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14) If 1 ounce = 28.3 grams, how many ounces are in 439 centigrams?

15) A temperature of 14°F is what temperature in °C?

16) A temperature of 71°C is what temperature in °F?

17) A temperature of 312°C is what temperature in kelvins?

18) A 7.6 cm3 piece of metal has a mass of 65.588 g. Calculate its density.

19) Find the mass of 58.8 mL of a solution having a density of 1.16 g/mL.

Answers to Chapter 3 Sample Test

1) 413,400 = 4.13400 ¥ 105 6.91 ¥ 107 = 69,100,0000.00103 = 1.03 ¥ 10– 3 1.47 ¥ 10– 4 = 0.000147

2) 4.1 ¥ 10– 6 + 1.59 ¥ 10– 5 = 2.00 ¥ 10– 5

6.7 ¥ 103 + 2.61 ¥ 104 = 3.28 ¥ 104

7.14 ¥ 103 – 3.9 ¥ 102 = 6.75 ¥ 103

8.34 ¥ 10– 1 – 3.6 ¥ 10– 2 = 7.98 ¥ 10– 1



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3) (1.16 ¥ 10– 3)(6.32 ¥ 10–11) = 7.33 ¥ 10–14

(4.62 ¥ 10– 6)(2.17 ¥ 108) = 1.00 ¥ 103

†

(9.76 ¥ 107)(8.17 ¥ 103)(1.23 ¥ 101)

= 6.48 ¥ 101 0

†

4.39 ¥ 104

(107)(7.11 ¥ 101) = – 5.77

4) At the Lagrange points, as well as anywhere else in the universe, a 70 kg person hasa mass of 70 kg. When there is no gravity, the person has no weight.

5) The measured quantity 0.099 gram has two significant figures.

6) To three significant figures, 2.6034 kilometers rounds to 2.60 kilometers.

7) 1 6 . 0 8 0 . 0 4 31 2 1 . 8 0 7 . 9 9 4 6 31 4 5 . 9 1 7 6 3 = 145.92

8) 2.193 ¥

†

5.8764.88

¥

†

0.06564.06

= 0.0027

9) GIVEN: 3 months WANTED: dollars

PER/PATH: months

†

4.33 weeks/monthæ Æ æ æ æ æ æ æ æ weeks

†

13.6 hours/weekæ Æ æ æ æ æ æ æ hours

†

6.45 dollars/houræ Æ æ æ æ æ æ æ æ dollars

3 months ¥

†

4.33 weeksmonth

¥

†

13.6 hoursweek

¥

†

6.45 dollarshour

= 1139 dollars

10) GIVEN: 45.0 in. WANTED: cm

PER/PATH: in.

†

2.54 cm/in.æ Æ æ æ æ æ cm

45.0 in. ¥

†

2.54 cmin.

= 114 cm

11) GIVEN: 40.1 m WANTED: mm

PER/PATH: m

†

1000 mm/mæ Æ æ æ æ æ æ mm

40.1 m ¥

†

1000 mmm

= 4.01 ¥ 104 mm



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12) GIVEN: 9.45 km WANTED: m

PER/PATH: km

†

1000 m/kmæ Æ æ æ æ æ m

9.45 km ¥

†

1000 mkm

= 9.45 ¥ 103 m

13) GIVEN: 3440 cm3 WANTED: qt

PER/PATH: cm3

†

1 mL/1 cm3

æ Æ æ æ æ æ æ mL

†

1000 mL/Læ Æ æ æ æ æ L

†

1.06 qt/Læ Æ æ æ æ æ qt

3440 cm3 ¥

†

1 mL1 cm3 ¥

†

1 L1000 mL

¥

†

1.06 qtL

= 3.65 qt

14) GIVEN: 439 cg WANTED: oz

PER/PATH: cg

†

100 cg/gæ Æ æ æ æ g

†

28.3 g/ozæ Æ æ æ æ æ oz

439 cg ¥

†

1 g100 cg

¥

†

1 oz28.3 g

= 0.155 oz

15) GIVEN: 14°F WANTED: T°C

EQUATION: T°C =

†

T°F – 321.8

=

†

14 – 321.8

= –10°C

16) GIVEN: 71°C WANTED: T°F

EQUATION: T°F = 1.8 T°C + 32 = 1.8(71) + 32 = 160°F

17) GIVEN: 312°C WANTED: TK

EQUATION: TK = T°C + 273 = 312 + 273 = 585 K

18) GIVEN: 7.6 cm3; 65.588 g WANTED: Density (assume g/cm3)

EQUATION: D ≡

†

mV

=

†

65.588 g7.6 cm3 = 8.6 g/cm3

19) GIVEN: 58.8 mL WANTED: mass (assume g)

PER/PATH: mL

†

1.16 g/mLæ Æ æ æ æ æ g

58.8 mL ¥

†

1.16 gmL

= 68.2 g

Chapter 3€¦ · · 2009-11-05C. Units made up of base units are derived units D. SI details in...

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Transcript of Chapter 3€¦ · · 2009-11-05C. Units made up of base units are derived units D. SI details in...