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End Show © Copyright Pearson Prentice Hall Slide 1 of 48 3.1 Measurements and Their Uncertainty On January 4, 2004, the Mars Exploration Rover Spirit landed on Mars. Each day of its mission, Spirit recorded measurements for analysis. In the chemistry laboratory, you must strive for accuracy and precision in your measurements.

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End Show © Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 2 of 48 Using and Expressing Measurements How do measurements relate to science? 3.1

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End Show © Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 3 of 48 3.1 Using and Expressing Measurements A measurement is a quantity that has both a number and a unit. Measurements are fundamental to the experimental sciences. For that reason, it is important to be able to make measurements and to decide whether a measurement is correct.

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End Show © Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 4 of 48 3.1 Using and Expressing Measurements In scientific notation, a given number is written as the product of two numbers: a coefficient and 10 raised to a power. The number of stars in a galaxy is an example of an estimate that should be expressed in scientific notation.

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End Show © Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 5 of 48 Accuracy, Precision, and Error How do you evaluate accuracy and precision? 3.1

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End Show © Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 6 of 48 3.1 Accuracy, Precision, and Error Accuracy and Precision Accuracy is a measure of how close a measurement comes to the actual or true value of whatever is measured. Precision is a measure of how close a series of measurements are to one another.

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End Show © Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 7 of 48 3.1 Accuracy, Precision, and Error To evaluate the accuracy of a measurement, the measured value must be compared to the correct value. To evaluate the precision of a measurement, you must compare the values of two or more repeated measurements.

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End Show © Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 8 of 48 3.1 Accuracy, Precision, and Error

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End Show © Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 9 of 48 3.1 Accuracy, Precision, and Error Determining Error The accepted value is the correct value based on reliable references. The experimental value is the value measured in the lab. The difference between the experimental value and the accepted value is called the error.

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End Show © Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 10 of 48 3.1 Accuracy, Precision, and Error The percent error is the absolute value of the error divided by the accepted value, multiplied by 100%.

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End Show © Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 11 of 48 Accuracy, Precision, and Error 3.1

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End Show © Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 12 of 48 3.1 Accuracy, Precision, and Error Just because a measuring device works, you cannot assume it is accurate. The scale below has not been properly zeroed, so the reading obtained for the person’s weight is inaccurate.

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End Show © Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 13 of 48 Significant Figures in Measurements Why must measurements be reported to the correct number of significant figures? 3.1

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End Show © Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 14 of 48 Significant Figures in Measurements Suppose you estimate a weight that is between 2.4 lb and 2.5 lb to be 2.46 lb. The first two digits (2 and 4) are known. The last digit (6) is an estimate and involves some uncertainty. All three digits convey useful information, however, and are called significant figures. The significant figures in a measurement include all of the digits that are known, plus a last digit that is estimated. 3.1

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End Show © Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 15 of 48 Significant Figures in Measurements Measurements must always be reported to the correct number of significant figures because calculated answers often depend on the number of significant figures in the values used in the calculation. 3.1

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End Show © Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 16 of 48 Significant Figures in Measurements 3.1

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End Show © Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 17 of 48 Significant Figures in Measurements 3.1

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End Show © Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 18 of 48 Significant Figures in Measurements 3.1

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© Copyright Pearson Prentice Hall End Show Slide 19 of 48

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© Copyright Pearson Prentice Hall Slide 20 of 48 End Show Practice Problems for Conceptual Problem 3.1

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End Show © Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 21 of 48 Significant Figures in Calculations How does the precision of a calculated answer compare to the precision of the measurements used to obtain it? 3.1

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End Show Slide 22 of 48 © Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Significant Figures in Calculations In general, a calculated answer cannot be more precise than the least precise measurement from which it was calculated. The calculated value must be rounded to make it consistent with the measurements from which it was calculated. 3.1

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End Show © Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 23 of 48 3.1 Significant Figures in Calculations Rounding To round a number, you must first decide how many significant figures your answer should have. The answer depends on the given measurements and on the mathematical process used to arrive at the answer.

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End Show © Copyright Pearson Prentice Hall SAMPLE PROBLEM Slide 24 of 48 3.1

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© Copyright Pearson Prentice Hall Slide 25 of 48 End Show Practice Problems for Sample Problem 3.1

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End Show © Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 26 of 48 3.1 Significant Figures in Calculations Addition and Subtraction The answer to an addition or subtraction calculation should be rounded to the same number of decimal places (not digits) as the measurement with the least number of decimal places.

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End Show © Copyright Pearson Prentice Hall SAMPLE PROBLEM Slide 27 of 48 3.2

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© Copyright Pearson Prentice Hall Slide 28 of 48 End Show Practice Problems for Sample Problem 3.2

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End Show © Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 29 of 48 3.1 Significant Figures in Calculations Multiplication and Division In calculations involving multiplication and division, you need to round the answer to the same number of significant figures as the measurement with the least number of significant figures. The position of the decimal point has nothing to do with the rounding process when multiplying and dividing measurements.

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End Show © Copyright Pearson Prentice Hall SAMPLE PROBLEM Slide 30 of 48 3.3

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© Copyright Pearson Prentice Hall Slide 31 of 48 End Show Practice Problems for Sample Problem 3.3

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© Copyright Pearson Prentice Hall Slide 32 of 48 End Show 3.1 Section Quiz 1. In which of the following expressions is the number on the left NOT equal to the number on the right? a.0.00456 X 10 –8 = 4.56 X 10 –11 b.454 X 10 –8 = 4.54 X 10 –6 c.842.6 X 10 4 = 8.426 X 10 6 d.0.00452 X 10 6 = 4.52 X 10 9

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© Copyright Pearson Prentice Hall Slide 33 of 48 End Show 3.1 Section Quiz 2. Which set of measurements of a 2.00-g standard is the most precise? a.2.00 g, 2.01 g, 1.98 g b.2.10 g, 2.00 g, 2.20 g c.2.02 g, 2.03 g, 2.04 g d.1.50 g, 2.00 g, 2.50 g

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© Copyright Pearson Prentice Hall Slide 34 of 48 End Show 3. A student reports the volume of a liquid as 0.0130 L. How many significant figures are in this measurement? a.2 b.3 c.4 d.5 3.1 Section Quiz

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© Copyright Pearson Prentice Hall Slide 35 of 48 End Show 3.2 The International System of Units In the signs shown here, the distances are listed as numbers with no units attached. Without the units, it is impossible to communicate the measurement to others. When you make a measurement, you must assign the correct units to the numerical value.

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© Copyright Pearson Prentice Hall Slide 36 of 48 End Show Measuring with SI Units Which five SI base units do chemists commonly use? 3.2

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© Copyright Pearson Prentice Hall Slide 37 of 48 End Show 3.2 Measuring with SI Units a.All measurements depend on units that serve as reference standards. The standards of measurement used in science are those of the metric system. b.The International System of Units (abbreviated SI, after the French name, Le Système International d’Unités) is a revised version of the metric system.

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© Copyright Pearson Prentice Hall Slide 38 of 48 End Show 3.2 Measuring with SI Units a.The five SI base units commonly used by chemists are the meter, the kilogram, the kelvin, the second, and the mole.

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© Copyright Pearson Prentice Hall Slide 39 of 48 End Show 3.2 Units and Quantities What metric units are commonly used to measure length, volume, mass, temperature and energy?

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© Copyright Pearson Prentice Hall Slide 40 of 48 End Show 3.2 Units and Quantities Units of Length a.In SI, the basic unit of length, or linear measure, is the meter (m). For very large or and very small lengths, it may be more convenient to use a unit of length that has a prefix.

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© Copyright Pearson Prentice Hall Slide 41 of 48 End Show 3.2 Units and Quantities Common metric units of length include the centimeter, meter, and kilometer.

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© Copyright Pearson Prentice Hall Slide 42 of 48 End Show 3.2 Units and Quantities Units of Volume a.The SI unit of volume is the amount of space occupied by a cube that is 1 m along each edge. This volume is the cubic meter (m) 3. A more convenient unit of volume for everyday use is the liter, a non- SI unit. b.A liter (L) is the volume of a cube that is 10 centimeters (10 cm) along each edge (10 cm 10 cm 10 cm = 1000 cm 3 = 1 L).

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© Copyright Pearson Prentice Hall Slide 43 of 48 End Show 3.2 Units and Quantities Common metric units of volume include the liter, milliliter, cubic centimeter, and microliter.

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© Copyright Pearson Prentice Hall Slide 44 of 48 End Show 3.2 Units and Quantities a.The volume of 20 drops of liquid from a medicine dropper is approximately 1 mL.

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© Copyright Pearson Prentice Hall Slide 45 of 48 End Show 3.2 Units and Quantities a.A sugar cube has a volume of 1 cm 3. 1 mL is the same as 1 cm 3.

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© Copyright Pearson Prentice Hall Slide 46 of 48 End Show 3.2 Units and Quantities a.A gallon of milk has about twice the volume of a 2-L bottle of soda.

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© Copyright Pearson Prentice Hall Slide 47 of 48 End Show 3.2 Units and Quantities Units of Mass a.The mass of an object is measured in comparison to a standard mass of 1 kilogram (kg), which is the basic SI unit of mass. b.A gram (g) is 1/1000 of a kilogram; the mass of 1 cm 3 of water at 4°C is 1 g.

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© Copyright Pearson Prentice Hall Slide 48 of 48 End Show 3.2 Units and Quantities Common metric units of mass include kilogram, gram, milligram, and microgram.

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© Copyright Pearson Prentice Hall Slide 49 of 48 End Show 3.2 Units and Quantities a.Weight is a force that measures the pull on a given mass by gravity. b.The astronaut shown on the surface of the moon weighs one sixth of what he weighs on Earth.

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© Copyright Pearson Prentice Hall Slide 50 of 48 End Show 3.2 Units and Quantities Units of Temperature a.Temperature is a measure of how hot or cold an object is. b.Thermometers are used to measure temperature.

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© Copyright Pearson Prentice Hall Slide 51 of 48 End Show 3.2 Units and Quantities Scientists commonly use two equivalent units of temperature, the degree Celsius and the kelvin.

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© Copyright Pearson Prentice Hall Slide 52 of 48 End Show 3.2 Units and Quantities a.On the Celsius scale, the freezing point of water is 0°C and the boiling point is 100°C. b.On the Kelvin scale, the freezing point of water is 273.15 kelvins (K), and the boiling point is 373.15 K. c.The zero point on the Kelvin scale, 0 K, or absolute zero, is equal to 273.15 °C.

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© Copyright Pearson Prentice Hall Slide 53 of 48 End Show 3.2 Units and Quantities a.Because one degree on the Celsius scale is equivalent to one kelvin on the Kelvin scale, converting from one temperature to another is easy. You simply add or subtract 273, as shown in the following equations.

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© Copyright Pearson Prentice Hall Slide 54 of 48 End Show 3.2 Units and Quantities a.Conversions Between the Celsius and Kelvin Scales

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© Copyright Pearson Prentice Hall Slide 55 of 48 End Show 3.4

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© Copyright Pearson Prentice Hall Slide 56 of 48 End Show 3.4

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© Copyright Pearson Prentice Hall Slide 57 of 48 End Show for Sample Problem 3.4

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© Copyright Pearson Prentice Hall Slide 58 of 48 End Show 3.2 Units and Quantities Units of Energy a.Energy is the capacity to do work or to produce heat. The joule and the calorie are common units of energy.

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© Copyright Pearson Prentice Hall Slide 59 of 48 End Show 3.2 Units and Quantities a.The joule (J) is the SI unit of energy. b.One calorie (cal) is the quantity of heat that raises the temperature of 1 g of pure water by 1°C.

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© Copyright Pearson Prentice Hall Slide 60 of 48 End Show 3.2 Units and Quantities a.This house is equipped with solar panels. The solar panels convert the radiant energy from the sun into electrical energy that can be used to heat water and power appliances.

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© Copyright Pearson Prentice Hall Slide 61 of 48 End Show 3.2 Section Quiz. 1. Which of the following is not a base SI unit? a.meter b.gram c.second d.mole

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© Copyright Pearson Prentice Hall Slide 62 of 48 End Show 3.2 Section Quiz. 2. If you measured both the mass and weight of an object on Earth and on the moon, you would find that a.both the mass and the weight do not change. b.both the mass and the weight change. c.the mass remains the same, but the weight changes. d.the mass changes, but the weight remains the same.

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© Copyright Pearson Prentice Hall Slide 63 of 48 End Show 3.2 Section Quiz. 3. A temperature of 30 degrees Celsius is equivalent to a.303 K. b.300 K. c.243 K. d.247 K.

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© Copyright Pearson Prentice Hall Slide 64 of 48 End Show 3.3 3 Conversion Problems Because each country’s currency compares differently with the U.S. dollar, knowing how to convert currency units correctly is very important. Conversion problems are readily solved by a problem- solving approach called dimensional analysis.

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© Copyright Pearson Prentice Hall Slide 65 of 48 End Show Conversion Factors What happens when a measurement is multiplied by a conversion factor? 3.3

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© Copyright Pearson Prentice Hall Slide 66 of 48 End Show 3.3 Conversion Factors a.A conversion factor is a ratio of equivalent measurements. b.The ratios 100 cm/1 m and 1 m/100 cm are examples of conversion factors.

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© Copyright Pearson Prentice Hall Slide 67 of 48 End Show 3.3 Conversion Factors When a measurement is multiplied by a conversion factor, the numerical value is generally changed, but the actual size of the quantity measured remains the same.

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© Copyright Pearson Prentice Hall Slide 68 of 48 End Show 3.3 Conversion Factors a.The scale of the micrograph is in nanometers. Using the relationship 10 9 nm = 1 m, you can write the following conversion factors.

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© Copyright Pearson Prentice Hall Slide 69 of 48 End Show 3.3 Dimensional Analysis Why is dimensional analysis useful?

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© Copyright Pearson Prentice Hall Slide 70 of 48 End Show 3.3 Dimensional Analysis a.Dimensional analysis is a way to analyze and solve problems using the units, or dimensions, of the measurements. Dimensional analysis provides you with an alternative approach to problem solving.

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© Copyright Pearson Prentice Hall Slide 71 of 48 End Show 3.5

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© Copyright Pearson Prentice Hall Slide 72 of 48 End Show for Sample Problem 3.5

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© Copyright Pearson Prentice Hall Slide 73 of 48 End Show 3.6

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© Copyright Pearson Prentice Hall Slide 74 of 48 End Show For Sample Problem 3.6 for Sample Problem 3.6

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© Copyright Pearson Prentice Hall Slide 75 of 48 End Show Converting Between Units What types of problems are easily solved by using dimensional analysis? 3.3

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© Copyright Pearson Prentice Hall Slide 76 of 48 End Show Converting Between Units Problems in which a measurement with one unit is converted to an equivalent measurement with another unit are easily solved using dimensional analysis. 3.3

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© Copyright Pearson Prentice Hall Slide 77 of 48 End Show 3.7

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© Copyright Pearson Prentice Hall Slide 78 of 48 End Show 3.7

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© Copyright Pearson Prentice Hall Slide 79 of 48 End Show for Sample Problem 3.7

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© Copyright Pearson Prentice Hall Slide 80 of 48 End Show Converting Between Units Multistep Problems a.When converting between units, it is often necessary to use more than one conversion factor. Sample problem 3.8 illustrates the use of multiple conversion factors. 3.3

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© Copyright Pearson Prentice Hall Slide 81 of 48 End Show 3.8

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© Copyright Pearson Prentice Hall Slide 82 of 48 End Show for Sample Problem 3.8

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© Copyright Pearson Prentice Hall Slide 83 of 48 End Show 3.3 Converting Between Units Converting Complex Units a.Many common measurements are expressed as a ratio of two units. If you use dimensional analysis, converting these complex units is just as easy as converting single units. It will just take multiple steps to arrive at an answer.

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© Copyright Pearson Prentice Hall Slide 84 of 48 End Show 3.9

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© Copyright Pearson Prentice Hall Slide 85 of 48 End Show for Sample Problem 3.9

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© Copyright Pearson Prentice Hall Slide 86 of 48 End Show 1. 1 Mg = 1000 kg. Which of the following would be a correct conversion factor for this relationship? a.x 1000. b.x 1/1000. c.÷ 1000. d.1000 kg/1Mg. 3.3 Section Quiz

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© Copyright Pearson Prentice Hall Slide 87 of 48 End Show 3.3 Section Quiz 2. The conversion factor used to convert joules to calories changes a.the quantity of energy measured but not the numerical value of the measurement. b.neither the numerical value of the measurement nor the quantity of energy measured. c.the numerical value of the measurement but not the quantity of energy measured. d.both the numerical value of the measurement and the quantity of energy measured.

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© Copyright Pearson Prentice Hall Slide 88 of 48 End Show 3.3 Section Quiz 3. Express the density 5.6 g/cm 3 in kg/m 3. a.5.6 x 10 6 kg/m 3 b.5.6 x 10 3 kg/m 3 c.0.56 kg/m 3 d.0.0056 kg/m 3

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© Copyright Pearson Prentice Hall Slide 89 of 48 End Show Density If you think that these lily pads float because they are lightweight, you are only partially correct. The ratio of the mass of an object to its volume can be used to determine whether an object floats or sinks in water. 3.4

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© Copyright Pearson Prentice Hall Slide 90 of 48 End Show Determining Density What determines the density of a substance? 3.4

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© Copyright Pearson Prentice Hall Slide 91 of 48 End Show Determining Density a.Density is the ratio of the mass of an object to its volume. 3.4

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© Copyright Pearson Prentice Hall Slide 92 of 48 End Show Determining Density a.Each of these 10-g samples has a different volume because the densities vary. 3.4

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© Copyright Pearson Prentice Hall Slide 93 of 48 End Show Determining Density Density is an intensive property that depends only on the composition of a substance, not on the size of the sample. 3.4

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© Copyright Pearson Prentice Hall Slide 94 of 48 End Show Determining Density a.The density of corn oil is less than the density of corn syrup. For that reason, the oil floats on top of the syrup. 3.4

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© Copyright Pearson Prentice Hall Slide 95 of 48 End Show Density and Temperature How does a change in temperature affect density? 3.4

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© Copyright Pearson Prentice Hall Slide 96 of 48 End Show Density and Temperature a.Experiments show that the volume of most substances increases as the temperature increases. Meanwhile, the mass remains the same. Thus, the density must change. The density of a substance generally decreases as its temperature increases. 3.4

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© Copyright Pearson Prentice Hall Slide 97 of 48 End Show 3.10

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© Copyright Pearson Prentice Hall Slide 98 of 48 End Show for Sample Problem 3.10

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© Copyright Pearson Prentice Hall Slide 99 of 48 End Show 3.11

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© Copyright Pearson Prentice Hall Slide 100 of 48 End Show for Sample Problem 3.11

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© Copyright Pearson Prentice Hall Slide 101 of 48 End Show 3.4 Section Quiz 1. If 50.0 mL of corn syrup have a mass of 68.7 g, the density of the corn syrup is a.0.737 g/mL. b.0.727 g/mL. c.1.36 g/mL. d.1.37 g/mL.

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© Copyright Pearson Prentice Hall Slide 102 of 48 End Show 3.4 Section Quiz 2. What is the volume of a pure gold coin that has a mass of 38.6 g? The density of gold is 19.3 g/cm 3. a.0.500 cm 3 b.2.00 cm 3 c.38.6 cm 3 d.745 cm 3

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© Copyright Pearson Prentice Hall Slide 103 of 48 End Show 3.4 Section Quiz 3. As the temperature increases, the density of most substances a.increases. b.decreases. c.remains the same. d.increases at first and then decreases.

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