Solving Problems: A Chemistry Handbook

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CHAPTER1SOLVING PROBLEMS:A CHEMISTRY HANDBOOKIntroduction to ChemistryCopyright Glencoe/McGraw-Hill, a division of the McGraw-Hill Companies, Inc.1.1 The Stories of Two ChemicalsA chemical is any substance that has a definite composition. Ozoneis a chemical that is made up of three particles of oxygen. Ozoneforms a thick blanket above the clouds in the stratosphere. This layerof ozone protects Earth from overexposure to ultraviolet radiationfrom the Sun. You are probably familiar with the damage that exposure to ultraviolet radiation can do to your skin in the form ofsunburn. Ultraviolet radiation can also harm other animals andplants. In the 1980s, scientists documented that the ozone layeraround Earth was becoming measurably thinner in some spots.In the 1970s, scientists had observed that large quantities ofchlorofluorocarbons (CFCs) had accumulated in Earth’s atmosphere.CFCs are chemicals that contain chlorine, fluorine, and carbon.CFCs were used as coolants in refrigerators and air conditioners andas propellants in spray cans because they were considered relativelynonreactive. Some scientists hypothesized that there might be a connection between the concentration of CFCs in the atmosphere andthe thinning of the ozone layer.1.2 Chemistry and MatterChemistry is the study of matter and the changes that it undergoes.Matter is anything that has mass and takes up space. Mass is ameasurement of the amount of matter in an object. Everything, however, is not made of matter. For example, heat, light, radio waves,and magnetic fields are some things that are not made of matter.You might wonder why scientists measure matter in terms ofmass, and not in terms of weight. Your body is made of matter, andyou probably weigh yourself in pounds. However, your weight isnot just a measure of the amount of matter in your body. Yourweight also includes the effect of Earth’s gravitational pull on yourbody. This force is not the same everywhere on Earth. Scientists usemass to measure matter instead of weight because they need to compare measurements taken in different locations.Solving Problems: A Chemistry HandbookChemistry: Matter and Change1

CHAPTER1SOLVING PROBLEMS:A CHEMISTRY HANDBOOKMatter is made up of particles, called atoms, that are so smallthey cannot be seen with an ordinary light microscope. The structure, composition, and behavior of all matter can be explained byatoms and the changes they undergo.Because there are so many types of matter, there are many areasof study in the field of chemistry. Chemistry is usually divided intofive branches, as summarized in the table below.Branches of ChemistryArea of emphasisExamplesOrganicchemistrymost Inorganicchemistryin general, matter thatdoes not contain carbonminerals, metals andnonmetals, semiconductorsPhysicalchemistrythe behavior and changesof matter and the relatedenergy changesreaction rates,reaction mechanismsAnalyticalchemistrycomponents andcomposition of substancesfood nutrients,quality controlBiochemistrymatter and processesof living organismsmetabolism,fermentation1.3 Scientific MethodsA scientific method is a systematic approach used to answer a question or study a situation. It is both an organized way for scientists todo research and a way for scientists to verify the work of other scientists. A typical scientific method includes making observations,forming a hypothesis, performing an experiment, and arriving at aconclusion.Scientific study usually begins with observations. Often, a scientist will begin with qualitative data—information that describescolor, odor, shape, or some other physical characteristic that relates tothe five senses. Chemists also use quantitative data. This type ofdata is numerical. It tells how much, how little, how big, or how fast.2Chemistry: Matter and ChangeSolving Problems: A Chemistry HandbookCopyright Glencoe/McGraw-Hill, a division of the McGraw-Hill Companies, Inc.Branch

CHAPTER1SOLVING PROBLEMS:A CHEMISTRY HANDBOOKCopyright Glencoe/McGraw-Hill, a division of the McGraw-Hill Companies, Inc.Practice Problems1. Identify each of the following as an example of qualitative dataor quantitative data.a. taste of an appled. length of a rodb. mass of a bricke. texture of a leafc. speed of a carf. weight of an elephantA hypothesis is a possible explanation for what has been observed.Based on the observations of ozone thinning and CFC buildup in theatmosphere, the chemists Mario Molina and F. Sherwood Rowlandhypothesized that CFCs break down in the atmosphere due to theSun’s ultraviolet rays. They further hypothesized that a chlorine particle produced by the breakdown of CFCs could break down ozone.An experiment is a set of controlled observations that test ahypothesis. In an experiment, a scientist will set up and change onevariable at a time. A variable is a quantity that can have more thanone value. The variable that is changed in an experiment is calledthe independent variable. The variable that you watch to see how itchanges as a result of your changes to the independent variable iscalled the dependent variable. For example, if you wanted to testthe effect of fertilizer on plant growth, you would change theamount of fertilizer applied to the same kinds of plants. The amountof fertilizer applied would be the independent variable in thisexperiment. Plant growth would be the dependent variable. Manyexperiments also include a control, which is a standard forcomparison; in this case, plants to which no fertilizer is applied.A conclusion is a judgment based on the data obtained in theexperiment. If data support a hypothesis, the hypothesis is tentativelyaffirmed. Hypotheses are never proven; they are always subject toadditional research. If additional data do not support a hypothesis, thehypothesis is discarded or modified. Most hypotheses are not supported by data. Whether the hypothesis is supported or not, the datacollected may still be useful. Over time, data from many experimentscan be used to form a visual, verbal, and/or mathematical explanation—called a model—of the phenomenon being studied.A theory is an explanation that has been supported by manyexperiments. Theories state broad principles of nature. Although theories are the best explanations of phenomena that scientists have atSolving Problems: A Chemistry HandbookChemistry: Matter and Change3

CHAPTER1SOLVING PROBLEMS:A CHEMISTRY HANDBOOKany given time, they are always subject to new experimental dataand are modified to include new data.A scientific law describes a relationship in nature that is supported by many experiments and for which no exception has beenfound. Scientists may use models and theories to explain why thisrelationship exists.1.4 Scientific ResearchPure research is done to gain knowledge for the sake of knowledgeitself. Molina and Rowland’s research on the behavior of CFCs—showing that in the lab CFCs could speed up the breakdown ofozone—was motivated by their curiosity and is an example of pureresearch. Applied research is undertaken to solve a specific problem. Scientists are conducting experiments to find chemicals toreplace CFCs. These experiments are examples of applied research.Safety in the Laboratory1. Study your lab assignment before you come to the lab. If youhave any questions, be sure to ask your teacher for help.2. Do not perform experiments without your teacher’s permission.Never work alone in the laboratory.3. Use the table on the inside front cover of this textbook tounderstand the safety symbols. Read all CAUTION statements.4. Safety goggles and a laboratory apron must be worn wheneveryou are in the lab. Gloves should be worn whenever you usechemicals that cause irritations or can be absorbed through theskin. Long hair must be tied back.5. Do not wear contact lenses in the lab, even under goggles.Lenses can absorb vapors and are difficult to remove in case ofan emergency.6. Avoid wearing loose, draping clothing and dangling jewelry. Barefeet and sandals are not permitted in the lab.7. Eating, drinking, and chewing gum are not allowed in the lab.8. Know where to find and how to use the fire extinguisher, safetyshower, fire blanket, and first-aid kit.4Chemistry: Matter and ChangeSolving Problems: A Chemistry HandbookCopyright Glencoe/McGraw-Hill, a division of the McGraw-Hill Companies, Inc. Laboratory safety During your study of chemistry, you willconduct experiments in the laboratory. When working in the lab, youare responsible for the safety of yourself and others working aroundyou. Each time you enter the lab, use these safety rules as a guide.

CHAPTER1SOLVING PROBLEMS:A CHEMISTRY HANDBOOKSafety in the Laboratory, continued9. Report any accident, injury, incorrect procedure, or damagedequipment to your teacher.10. If chemicals come in contact with your eyes or skin, flush the areaimmediately with large quantities of water. Immediately informyour teacher of the nature of the spill.11. Handle all chemicals carefully. Check the labels of all bottlesbefore removing the contents. Read the label three times: Before you pick up the container. When the container is in your hand. When you put the bottle back.12. Do not take reagent bottles to your work area unless instructedto do so. Use test tubes, paper, or beakers to obtain yourchemicals. Take only small amounts. It is easier to get morethan to dispose of excess.13. Do not return unused chemicals to the stock bottle.14. Do not insert droppers into reagent bottles. Pour a small amountof the chemical into a beaker.15. Never taste any chemicals. Never draw any chemicals into apipette with your mouth.Copyright Glencoe/McGraw-Hill, a division of the McGraw-Hill Companies, Inc.16. Keep combustible materials away from open flames.17. Handle toxic and combustible gases only under the direction ofyour teacher. Use the fume hood when such materials are present.18. When heating a substance in a test tube, be careful not to pointthe mouth of the test tube at another person or yourself. Neverlook down the mouth of a test tube.19. Do not heat graduated cylinders, burettes, or pipettes with alaboratory burner.20. Use caution and proper equipment when handling hot apparatusor glassware. Hot glass looks the same as cool glass.21. Dispose of broken glass, unused chemicals, and products ofreactions only as directed by your teacher.22. Know the correct procedure for preparing acid solutions. Alwaysadd the acid slowly to the water.23. Keep the balance area clean. Never place chemicals directly on thepan of a balance.24. After completing an experiment, clean and put away yourequipment. Clean your work area. Make sure the gas and waterare turned off. Wash your hands with soap and water beforeyou leave the lab.Solving Problems: A Chemistry HandbookChemistry: Matter and Change5

1SOLVING PROBLEMS:A CHEMISTRY HANDBOOKChapter 1 Review2. How does the ozone layer protect Earth?3. Why did scientists think that the thinning of the ozone layermight be related to CFCs?4. Contrast mass and weight.5. During a chemistry lab, a student noted the following dataabout an unknown chemical she was studying: colorless,dissolves in water at room temperature, melts at 95 C, boils at800 C. Classify each piece of data as either qualitative data orquantitative data.6. Identify the dependent variable and the independent variable inthe following experiments.a. A student tests the ability of a given chemical to dissolve inwater at three different temperatures.b. A farmer compares how his crops grow with and withoutphosphorous fertilizers.c. An environmentalist tests the acidity of water samples at fivedifferent distances from a factory.7. Explain why hypotheses and theories are always tentativeexplanations.8. List two possible hypotheses about the relationship betweenozone and CFCs.9. Classify each kind of research as either pure or applied.a. A scientist studies plants in a rain forest in search ofchemicals that might be used to treat AIDS.b. A researcher studies the effects of hormones on the brain ofa worm.c. A researcher tries to develop cleaner burning fuels to helpreduce air pollution.10. State two rules you should follow when handling chemicals.11. How should you dispose of the following items in the lab:broken glass, products of chemical reactions, unusedchemicals?6Chemistry: Matter and ChangeSolving Problems: A Chemistry HandbookCopyright Glencoe/McGraw-Hill, a division of the McGraw-Hill Companies, Inc.CHAPTER

CHAPTER2SOLVING PROBLEMS:A CHEMISTRY HANDBOOKData Analysis2.1 Units of MeasurementYou probably know your height in feet and inches. Most peopleoutside the United States, however, measure height in meters andcentimeters. The system of standard units that includes the meter iscalled the metric system. Scientists today use a revised form of themetric system called the Système Internationale d’Unités, or SI. Base units There are seven base units in SI. A base unit is a unitof measure that is based on an object or event in the physical world.Table 2-1 lists the seven SI base units, their abbreviations, and thequantities they are used to measure.Table 2-1SI Base UnitsCopyright Glencoe/McGraw-Hill, a division of the McGraw-Hill Companies, Inc.QuantityBase unitTimesecond (s)Lengthmeter (m)Masskilogram (kg)Temperaturekelvin (K)Amount of asubstancemole (mol)Electric currentampere (A)Luminousintensitycandela (cd)SI is based on a decimal system. So are the prefixes in Table 2-2,which are used to extend the range of SI units.Solving Problems: A Chemistry HandbookChemistry: Matter and Change7

CHAPTER2SOLVING PROBLEMS:A CHEMISTRY HANDBOOKTable 2-2Prefixes Used with SI gaG1 000 000 000109gigameter (Gm)megaM1 000 000106megagram (Mg)kilok1000103kilometer (km)decid1/1010 1deciliter (dL)centic1/10010 2centimeter (cm)millim1/100010 3milligram (mg)micro 1/1 000 00010 6microgram ( g)nanon1/1 000 000 00010 9nanometer (nm)picop1/1 000 000 000 00010 12picometer (pm)Example Problem 2-1Using Prefixes with SI UnitsThe prefix pico- means 10 12, or 1/1 000 000 000 000. Thus, thereare 1012, or 1 000 000 000 000, picograms in one gram.Practice Problems1. How many centigrams are in a gram?2. How many liters are in a kiloliter?3. How many nanoseconds are in a second?4. How many meters are in a kilometer? Derived units Not all quantities can be measured using SI baseunits. For example, volume and density are measured using unitsthat are a combination of base units. An SI unit that is defined by acombination of base units is called a derived unit. The SI unit forvolume is the liter. A liter is a cubic meter, that is, a cube whosesides are all one meter in length. Density is a ratio that compares themass of an object to its volume. The SI units for density are oftengrams per cubic centimeter (g/cm3) or grams per milliliter (g/mL).One centimeter cubed is equivalent to one milliliter.8Chemistry: Matter and ChangeSolving Problems: A Chemistry HandbookCopyright Glencoe/McGraw-Hill, a division of the McGraw-Hill Companies, Inc.How many picograms are in a gram?

CHAPTER2SOLVING PROBLEMS:A CHEMISTRY HANDBOOKExample Problem 2-2Calculating DensityA 1.1-g ice cube raises the level of water in a 10-mL graduatedcylinder 1.2 mL. What is the density of the ice cube?To find the ice cube’s density, divide its mass by the volume ofwater it displaced and solve.density mass/volume1.1 gdensity 0.92 g/mL1.2 mLExample Problem 2-3Using Density and Volume to Find MassSuppose you drop a solid gold cube into a 10-mL graduatedcylinder containing 8.50 mL of water. The level of the water risesto 10.70 mL. You know that gold has a density of 19.3 g/cm3, or19.3 g/mL. What is the mass of the gold cube?Copyright Glencoe/McGraw-Hill, a division of the McGraw-Hill Companies, Inc.To find the mass of the gold cube, rearrange the equation for densityto solve for mass.density mass/volumemass volume densitySubstitute the values for volume and density into the equation andsolve for mass.mass 2.20 mL 19.3 g/mL 42.5 gPractice Problems5. Calculate the density of a piece of bone with a mass of 3.8 gand a volume of 2.0 cm3.6. A spoonful of sugar with a mass of 8.8 grams is poured into a10-mL graduated cylinder. The volume reading is 5.5 mL. Whatis the density of the sugar?7. A 10.0-gram pat of butter raises the water level in a 50-mLgraduated cylinder by 11.6 mL. What is the density of thebutter?Solving Problems: A Chemistry HandbookChemistry: Matter and Change9

CHAPTER2SOLVING PROBLEMS:A CHEMISTRY HANDBOOK8. A sample of metal has a mass of 34.65 g. When placed in agraduated cylinder containing water, the water level rises3.3 mL. Which of the following metals is the sample madefrom: silver, which has a density of 10.5 g/cm3; tin, which hasa density of 7.28 g/cm3; or titanium, which has a density of4.5 g/cm3?9. Rock salt has a density of 2.18 g/cm3. What would the volumebe of a 4.8-g sample of rock salt?10. A piece of lead displaces 1.5 mL of water in a graduatedcylinder. Lead has a density of 11.34 g/cm3. What is the massof the piece of lead?Practice Problems11. Convert each temperature reported in degrees Celsius tokelvins.a. 54 Cb. 54 Cc. 15 C12. Convert each temperature reported in kelvins to degreesCelsius.a. 32 Kb. 0 Kc. 281 K10Chemistry: Matter and ChangeSolving Problems: A Chemistry HandbookCopyright Glencoe/McGraw-Hill, a division of the McGraw-Hill Companies, Inc. Temperature The temperature of an object describes how hotor cold the object is relative to other objects. Scientists use two temperature scales—the Celsius scale and the Kelvin scale—to measuretemperature. You will be using the Celsius scale in most of yourexperiments. On the Celsius scale, the freezing point of water isdefined as 0 degrees and the boiling point of water is defined as100 degrees.A kelvin is the SI base unit of temperature. On the Kelvin scale,water freezes at about 273 K and boils at about 373 K. One kelvin isequal in size to one degree on the Celsius scale. To convert fromdegrees Celsius to kelvins, add 273 to the Celsius measurement.To convert from kelvins to degrees Celsius, subtract 273 from themeasurement in kelvins.

CHAPTER2SOLVING PROBLEMS:A CHEMISTRY HANDBOOK2.2 Scientific Notation and Dimensional AnalysisExtremely small and extremely large numbers can be comparedmore easily when they are converted into a form called scientificnotation. Scientific notation expresses numbers as a multiple of twofactors: a number between 1 and 10; and ten raised to a power, orexponent. The exponent tells you how many times the first factormust be multiplied by ten. When numbers larger than 1 areexpressed in scientific notation, the power of ten is positive. Whennumbers smaller than 1 are expressed in scientific notation, thepower of ten is negative. For example, 2000 is written as 2 103 inscientific notation, and 0.002 is written as 2 10 3.Example Problem 2-4Expressing Quantities in Scientific NotationCopyright Glencoe/McGraw-Hill, a division of the McGraw-Hill Companies, Inc.The surface area of the Pacific Ocean is 166 000 000 000 000 m2.Write this quantity in scientific notation.To write the quantity in scientific notation, move the decimal pointto after the first digit to produce a factor that is between 1 and 10.Then count the number of places you moved the decimal point; thisnumber is the exponent (n). Delete the extra zeros at the end of thefirst factor, and multiply the result by 10n. When the decimal pointmoves to the left, n is positive. When the decimal point moves to theright, n is negative. In this problem, the decimal point moves14 places to the left; thus, the quantity is written as 1.66 1014 inscientific notation.Practice Problems13. Express the following quantities in scientific notation.a. 50 000 m/s2b. 0.000 000 000 62 kgc. 0.000 023 sd. 21 300 000 mLe. 990 900 000 m/sf. 0.000 000 004 LSolving Problems: A Chemistry HandbookChemistry: Matter and Change11

CHAPTER2SOLVING PROBLEMS:A CHEMISTRY HANDBOOK Adding and subtracting using scientific notation To add orsubtract quantities written in scientific notation, the quantities musthave the same exponent. For example, 4.5 1014 m 2.1 1014 m 6.6 1014 m. If two quantities are expressed to different powersof ten, you must change one of the quantities so that they are bothexpressed to the same power of ten before you add or subtract them.Example Problem 2-5Adding Quantities Written in Scientific NotationSolve the following problem.2.45 1014 kg 4.00 1012 kgPractice Problems14. Solve the following addition and subtraction problems. Writeyour answers in scientific notation.a. 5.10 1020 4.11 1021b. 6.20 108 3.0 106c. 2.303 105 2.30 103d. 1.20 10 4 4.7 10 5e. 6.20 10 6 5.30 10 5f. 8.200 102 2.0 10 1 Multiplying and dividing using scientific notation Whenmultiplying or dividing quantities written in scientific notation, thequantities do not have to have the same exponent. For multiplication,multiply the first factors, then add the exponents. For division,divide the first factors, then subtract the exponents.Example Problem 2-6Multiplying Quantities Written in Scientific NotationSolve the following problem.(2 1014 cm) (4 1012 cm)12Chemistry: Matter and ChangeSolving Problems: A Chemistry HandbookCopyright Glencoe/McGraw-Hill, a division of the McGraw-Hill Companies, Inc.First express both quantities to the same power of ten. Either quantitycan be changed. For example, you might change 2.45 1014 to 245 1012. Then add the quantities: 245 1012 kg 4.00 1012 kg 249 1012 kg. Write the final answer in scientific notation: 2.49 1014 kg.

CHAPTER2SOLVING PROBLEMS:A CHEMISTRY HANDBOOKTo solve the multiplication problem, first multiply the factors:2 4 8. Then add the exponents: 14 12 26. Combine thefactors: 8 1026. Finally, multiply the units and write your answerin scientific notation: 8 1026 cm2.Practice Problems15. Solve the following multiplication and division problems. Writeyour answers in scientific notation.a. (12 104 m) (5 10 2 m)b. (3 107 km) (3 107 km)c. (2 10 4 mm) (2 10 4 mm)d. (90 1014 kg) (9 1012 L)e. (12 10 4 m) (3 10 4 s)f. (20 1015 km) (5 1011 s)Copyright Glencoe/McGraw-Hill, a division of the McGraw-Hill Companies, Inc. Dimensional analysis Dimensional analysis is a method ofproblem solving that focuses on the units that are used to describematter. Dimensional analysis often uses conversion factors. Aconversion factor is a ratio of equivalent values used to express thesame quantity in different units. A conversion factor is always equalto 1. Multiplying a quantity by a conversion factor does not changeits value—because it is the same as multiplying by 1—but the unitsof the quantity can change.Example Problem 2-7Converting From One Unit to Another UnitHow many centigrams are in 5 kilograms?Two conversion factors are needed to solve this problem. Rememberthat there are 1000 grams in a kilogram and 100 centigrams in agram. To determine the number of centigrams in 1 kilogram, set upthe first conversion factor so that kilograms cancel out. Set up thesecond conversion factor so that grams cancel out.100 cg1g5 kg 0.5 cg1000 kg1gSolving Problems: A Chemistry HandbookChemistry: Matter and Change13

CHAPTER2SOLVING PROBLEMS:A CHEMISTRY HANDBOOKPractice Problems16. Mount Everest is 8847 m high. How many centimeters high isthe mountain?17. Your friend is 1.56 m tall. How many millimeters tall is yourfriend?18. A family consumes 2.5 gallons of milk per week. How manyliters of milk do they need to buy for one week?(Hint: 1 L 0.908 quart; 1 gallon 4 quarts.)19. How many hours are there in one week? How many minutes arethere in one week?2.3 How reliable are measurements? Percent error Quantities measured during an experiment arecalled experimental values. The difference between an acceptedvalue and an experimental value is called an error. The ratio of anerror to an accepted value is called percent error. The equation forpercent error is as follows.errorPercent error 100accepted valueWhen you calculate percent error, ignore any plus or minus signsbecause only the size of the error counts.Example Problem 2-8Calculating Percent ErrorJuan calculated the density of aluminum three times.Trial 1: 2.74 g/cm3Trial 2: 2.68 g/cm3Trial 3: 2.84 g/cm314Chemistry: Matter and ChangeSolving Problems: A Chemistry HandbookCopyright Glencoe/McGraw-Hill, a division of the McGraw-Hill Companies, Inc.When scientists look at measurements, they want to know how accurate as well as how precise the measurements are. Accuracy refersto how close a measured value is to an accepted value. Precisionrefers to how close a series of measurements are to one another.Precise measurements might not be accurate, and accurate measurements might not be precise. When you make measurements, youwant to aim for both precision and accuracy.

CHAPTER2SOLVING PROBLEMS:A CHEMISTRY HANDBOOKAluminum has a density of 2.70 g/cm3. Calculate the percent errorfor each trial.First, calculate the error for each trial by subtracting Juan’s measurement from the accepted value (2.70 g/cm3).Trial 1: error 2.70 g/cm3 2.74 g/cm3 0.04 g/cm3Trial 2: error 2.70 g/cm3 2.68 g/cm3 0.02 g/cm3Trial 3: error 2.70 g/cm3 2.84 g/cm3 0.14 g/cm3Then, substitute each error and the accepted value into the percenterror equation. Ignore the plus and minus signs.0.04 g/cm3Trial 1: percent error 3 100 1.48%2.70 g/cm0.02 g/cm3Trial 2: percent error 3 100 0.741%2.70 g/cmCopyright Glencoe/McGraw-Hill, a division of the McGraw-Hill Companies, Inc.0.14 g/cm3Trial 3: percent error 3 100 5.19%2.70 g/cmPractice Problems20. Suppose you calculate your semester grade in chemistry as90.1, but you receive a grade of 89.4. What is your percenterror?21. On a bathroom scale, a person always weighs 2.5 pounds lessthan on the scale at the doctor’s office. What is the percent errorof the bathroom scale if the person’s actual weight is 125pounds?22. A length of wood has a labeled length value of 2.50 meters. Youmeasure its length three times. Each time you get the samevalue: 2.35 meters.a. What is the percent error of your measurements?b. Are your measurements precise? Are they accurate?Solving Problems: A Chemistry HandbookChemistry: Matter and Change15

CHAPTER2SOLVING PROBLEMS:A CHEMISTRY HANDBOOK Significant figures The number of digits reported in a measurement indicates how precise the measurement is. The more digitsreported, the more precise the measurement. The digits reported in ameasurement are called significant figures. Significant figuresinclude all known digits plus one estimated digit.These rules will help you recognize significant figures.1. Nonzero numbers are always significant.45.893421 min has eight significant figures2. Zeros between nonzero numbers are always significant.2001.5 km has five significant figures3. All final zeros to the right of the decimal place are significant.6.00 g has three significant figures4. Zeros that act as placeholders are not significant. You canconvert quantities to scientific notation to remove placeholderzeros.0.0089 g and 290 g each have two significant figures5. Counting numbers and defined constants have an infinite num-Example Problem 2-9Counting Significant FiguresHow many significant figures are in the following measurements?a. 0.002 849 kgb. 40 030 kgApply rules 1–4 from above. Check your answers by writing thequantities in scientific notation.a. 0.002 849 kg has four significant figures; 2.849 10 3b. 40 030 kg has four significant figures; 4.003 104Practice Problems23. Determine the number of significant figures in eachmeasurement.a. 0.000 010 Lc. 2.4050 10 4 kgb. 907.0 kmd. 300 100 000 g16Chemistry: Matter and ChangeSolving Problems: A Chemistry HandbookCopyright Glencoe/McGraw-Hill, a division of the McGraw-Hill Companies, Inc.ber of significant figures.

CHAPTER2SOLVING PROBLEMS:A CHEMISTRY HANDBOOKCopyright Glencoe/McGraw-Hill, a division of the McGraw-Hill Companies, Inc. Rounding off numbers When you report a calculation, youranswer should have no more significant figures than the piece ofdata you used in your calculation with the fewest number of significant figures. Thus, if you calculate the density of an object with amass of 12.33 g and a volume of 19.1 cm3, your answer should haveonly three significant figures. However, when you divide these quantities using your calculator, it will display 0.6455497—many morefigures than you can report in your answer. You will have to roundoff the number to three significant figures, or 0.646.Here are some rules to help you round off numbers.1. If the digit to the immediate right of the last significant figure isless than five, do not change the last significant figure.2. If the digit to the immediate right of the last significant figure isgreater than five, round up the last significant figure.3. If the digit to the immediate right of the last significant figure isequal to five and is followed by a nonzero digit, round up thelast significant figure.4. If the digit to the immediate right of the last significant figure isequal to five and is not followed by a nonzero digit, look at thelast significant figure. If it is an odd digit, round it up. If it is aneven digit, do not round up.Whether you are adding, subtracting, multiplying, or dividing, youmust always report your answer so that it has the same number ofsignificant figures as the measurement with the fewest significantfigures.Example Problem 2-10Rounding Off NumbersRound the following number to three significant figures: 3.4650.Rule 4 applies. The digit to the immediate right of the last significant figure is a 5 followed by a zero. Because the last significantfigure is an even digit (6), do not round up. The answer is 3.46.Solving Pro