Scientific measurement Chapter 3.1 Mr. Hines

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1 Scientific measurement Chapter 3.1 Mr. Hines Part A. The basics of measurement Learning Targets 1 Define measurement and list different ways that the universe can be measured. 2 Associate different measurements with their proper units. 3 Analyze measurement as a function of Accuracy and Precision. 4 Explain the Reasons for Error in Measurement. 5 Calculate percent error. I CAN Part B. Arithmetic of science and significant figures 6 Determine the numerical place value of whole numbers and decimal numbers. 7 Round numbers to the proper place value. 8 Make proper measurements using common tools in chemistry. 9 Estimate the uncertain digit. 10 Define significant figures and Explain why they are important. 11 Determine the significant figures in a measurement. 12 Add and subtract sig figs. 13 Multiply and Divide sig figs. Part C. Powers of 10 and scientific notation 14 Recall basic knowledge about powers of Define scientific notation, identify its parts, and explain why it is important. 16 Convert large numbers back and forth between scientific notation and standard form. 17 Convert small numbers back and forth between scientific notation and standard form. 18 Enter scientific notation into a calculator. 19 Multiply large and small numbers using scientific notation. 20 Divide large and small numbers using scientific notation. Part D Background Information About Conversions 21 Define conversion 22 Identify the different forms of conversions common in chemistry. 23 Identify the various units common in the English System. 24 Explain how the Metric system is organized with units. 25 Compare the metric system and the English system. 26 Identify abbreviations for measurements common in chemistry. Part E Calculations and Conversions 27 Perform unit conversions within the metric system. 28 Multiply fractions. 29 Understand mathematical cancellations. 30 Use dimensional analysis to convert back and forth between units in the English system and units in the metric system. 31 Convert various units of temperature English, metric, and SI. 32 Define Absolute Zero and explain how the Kelvin Temperature scale was developed. Part F Density 33 Describe/define density 34 Explain density as a measure of compactness. 35 Calculate the volume of various forms of matter including solid shapes cube, sphere, irregular using the metric system. 36 Explain the relationship between milliliters and cubic centimeters 37 Solve single variable algebraic equations 38 Calculate density 39 Calculate volume 40 Calculate mass 41 Explain density as a relationship between volume and particle spacing 42 Explain how objects of different sizes can have the same mass. 43 Explain how objects of the same size can have different masses. 44 Calculate the density of substances and predict which substances will float on which.

2 Vocabulary Parts A-C Measurement Unit Mass Volume Accuracy Precision Error Accepted value Chemistry Average Temperature English system SI system Metric system Second Kelvin Celsius Fahrenheit Gallon Liter Kilogram Gram Percent error Pound Significant figure Uncertainty Experimental value Decimal number Proper place value Scientific notation Inclusive Trailing zeros Decimal Matter Figure Digit Decimal places Place value Sig fig Sig dig Uncertain digit Dog Coefficient Power of 10 Atom Standard form Convert Exponent Energy Weight Percent Element Whole number Meniscus Space Time Universe Vocabulary Parts E-F Conversion Measurement Unit float Density Meter Prefix Length Dimensional analysis Conversion factor Cubic centimeter Irregular shape Absolute zero abbreviation Joule Base unit Toe cube Numerator Denominator Nothing Sphere Calorie Substance Compact Moon Solid Feet Liquid Milliliter Part A THE BASICS OF MEASUREMENT Target 1 - Define measurement and list different ways that the universe can be measured. Pg 64 A. Measurement - a quantity that has both a number and a unit. 1. For example, how much do you weigh? 2. In order for this to be a proper measurement, it must contain a number and a unit. B. Science is very dependent on measurements. C. Every time a scientist performs an experiment, something is being measured. D. The four things in the universe are commonly measured in chemistry. 1. Matter measured as mass or weight 2. Space measured as volume 3. Energy measured as temperature (energy has other measurements) 4. Time measured as time E. There is a very basic relationship between these 4 things in the universe. Energy moves matter through space and it takes some time. F. Everything everywhere is doing this. Questions 1. What is a measurement? 2. What are the 4 measurements common in chemistry? a) b) c) d) 3. What is the relationship between these 4 things measured in chemistry?

3 Target 2 - Associate different measurements with their proper units. Pg 73 A. The universe can be measured using many units. B. There are 3 systems for making measurements. 1. English System - used only in the United States 2. Metric System - Used around the world 3. SI System Used around the world in science (SI stands for System International ) Universe Measurement English unit Metric unit SI unit 1. Matter 2. Space 3. Energy 4, Time Target 3 - Analyze measurement as a function of Accuracy and Precision. Pg 64 A. Accuracy the closeness of a measurement to the true value of what is being measured. B. Precision the reproducibility of a measurement when it is repeated. Consider the example below: 3.1 Measurements and Their > Accuracy, Precision, and Error Uncertainty Slide 9 of 48 Copyright Pearson Prentice Hall Target 4 - Explain the Reasons for Error in Measurement. Pg 64 A. Accuracy in measurements 1. All sciences rely on. 2. Human beings of course are the ones who make the measurements. 3. Human beings are imperfect and make mistakes. 4. When mistakes are made, it is called. 5. Error mistake or accidental incorrectness 6. When humans make measurements, there are 2 factors that can cause error. a. The ability to properly read a measuring tool b. The quality of the measuring tool B. These 2 scenarios can both lead to ERROR 1. Example 1: A person can have a very accurate measuring tool and not know how to use it 2. Example 2: A person can be very skilled at measuring, but have poor measuring tools

4 Questions 1. What is accuracy? 2. What is precision? 3. What is error? 4. Describe the 2 scenarios that lead to error. a. b. Target 5 - Calculate percent error. Pg 65 A. Percent error 1. Percent error - a calculation that determines the of a person s measurement. 2. In other words, it can determine how correct or incorrect a measurement is. 3. There are 2 terms that you need to know in order to calculate percent error. a. Accepted value b. Experimental value 4. Accepted value the correct value based on reliable information. Information listed on a label of something is generally an accepted value. 5. Example, If you buy a gallon of milk, the container will say 1 Gallon This is the accepted value. 6. Experimental value a value that is measured in a lab (by you). B. Calculations 1. When taking scientific measurements, human beings make errors. The amount of error can be determined by simple mathematics. 2. This number should be written as a percent and gives a scientist an idea how accurate s(he) was. For example: The known value for the Lab table was 829 cm. Jack Belittle measured the lab table to be 813 cm. What is Jack s percent error? 829 cm 813 cm x 100 = 1.93% 829 cm **This says that Jack s measurement was off by 1.93% (not bad) Practice Percent error Accepted Value Experimental value Percent error 1) 255 milliliters 271 milliliters 2) 78.4 grams 82.6 grams 3) grams grams 4) 10.1 meters 9.12 meters 5).0675 liters.0758 liters Questions

5 1. Define accepted value 2. Define experimental value 3. What do you think causes some percents to be negative? 4. Kyle McIntyre is at Kroger and buys a gallon of orange juice. When he gets home, he measures the volume of the orange juice with various tools around the house. His measurement says that he has 1.2 gallons of orange juice. a. What is the accepted value? b. What is the experimental value? 5. Calculate the percent error of Kyle s measurement? Show your work. PART B THE ARITHMETIC OF SCIENCE AND SIGNIFICANT FIGURES Target 6 - Determine the numerical place value of whole numbers and decimal numbers. A. Number - an expression that represents the counting of (includes all digits) B. Whole number digits left of the decimal point C. Decimal number digits right of the decimal point (aka decimal place) D. Place value name of the place or location of a digit in a number E. Figure written symbol usually a part of a number F. Digit - written symbol usually a part of a number G. All figures (digits) will have a place value. Example 1 Notes label all words listed above Example Place value Before the decimal figure Place value After the decimal figure Hundreds place Tenth place Tens place Ones place Hundredth place Thousandth place Questions

6 Example What is the number listed in example 3? 2. Which figure represents the hundreds place? 3. Which figure represents the tens place? 4. Which figure represents the ones place? 5. Which figure represents the tenth place? 6. Which figure represents the hundredth place? 7. Which figure represents the thousandth place? 8. What is the synonym for figure? Target 7 Round numbers to the proper place value. A. Rounding numbers process where the amount of figures in a number is properly shortened. B. Proper place value place value that you should round to. C. There are 4 basic rules 1. The proper place value may or may not change 2. The figure that follows the proper place value will determine how to round. 3. Figures between 1 and 4 cause no change and are simply removed. 4. Figures between 5 and 9 will cause the proper place value to increase by 1. Notes Practice Number Proper place value Answer Number Proper place value Ones 9 Hundredth Ones 10 Hundredth Ones 11 Hundredth Ones 12 Hundredth Tenth 13 Tens Tenth 14 Ones 6.9 Tenth 15 Tenth 7.59 Tenth 16 Hundredth Answer Target 8 - Make proper measurements using common tools in chemistry. A. Tools for measurement in chemistry will measure the four things in the universe matter, energy, space, and time B. Reading a measuring tool properly takes and understanding. C. In order to read a measuring tool properly, you must understand how the decimal system works.

7 D. For this reason, the metric system must be used for all scientific measurements because the metric system is based on the. E. All units in the metric system can be divided by 10. (English system is based on fractions). F. To take a proper measurement from a lab tool, you must include one last digit past the smallest increment marked on the lab tool. G. Consider these examples - centimeters 1 Answer here Target 9 - Estimate the uncertain digit. A. All measuring tools have. B. Measuring tools can only measure to 1/10 of its smallest graduation. C. For example, the measuring tool shown below can measure accurately to the ones and tenths place value. D. It can also measure to the hundredths place based on the observer s. E. The uncertain digit is estimated as 1/10 of the smallest graduation. F. Uncertain digit last digit in a scientific measurement that is. G. A person s ability to measure properly is called accuracy. H. In order for a person to measure accurately, they must include an accurate uncertain digit. Target 10 - Define significant figures and Explain why they are important. Pg 66 A. Significant figure a count of all the digits that can be known accurately in a measurement, plus a last estimated digit. (aka sig figs) Ruler Z B. Lets assume that ruler Z (above) measures in centimeters. C. It is counting in the ones place, is graduated to measure in the tenths place, and therefore is limited to a last figure in the hundredths place. The measurement above would be 6.25 centimeters. D. It is improper to write a number beyond the measurement capability of the measuring tool. E. Therefore, a measurement like this ; has too many figures. The seven is insignificant because the measuring tool cannot measure to that place value. F The seven would therefore be used to round the final measurement to G. Why are significant figures important? 1. Significant figures will eliminate unnecessary numbers after the decimal. For example, enter this into your calculator 153 / You don t need all of these numbers where do you cut them off?

8 H. Significant figures are important because they express the accuracy of a measurement. (decimal place value) Questions This is a thermometer that measures degrees Celsius. 1. What is the accurate measurement for this measuring tool? 2. What place value is the uncertain digit? 5. Draw your own line on the thermometer to represent a measurement of 31.7 degrees Celsius. Target 11 Determine the significant figures in a measurement. 5 Golden Rules of Significant Figures 1. All digits 1-9 inclusive are significant. Example: 129 has 3 significant figures 2. Zeros between significant digits are always significant. Example: 5007 has 4 significant figures 3. Trailing zeros in a number are significant only if the number contains a decimal point Example: has 4 significant figures. 100 has 1 significant figure. 4. Zeros in the beginning of a number whose only function is to place the decimal point are not significant. Example: has 2 significant figures. 5. Zeros following a decimal significant figure are significant. Examples: has 3 significant figures has 5 significant figures. Rule 1 Sig figs Rule 4 Sig figs Rule 2 Rule

9 Rule 3 Review Target 12 Add and subtract sig figs. Pg 68 RULE: When adding or subtracting, your answer can only show as many decimal places as the measurement having the fewest number of decimal places. You must round to the proper place value. Write the number of decimal places above each number and then perform the mathematics. 1) = 7) ) = 8) = 3) = 9) = 4) = 10) = 5) = 11) = 6) = 12) = Target 13 Multiply and Divide sig figs. RULE: When multiplying or dividing, your answer may only show as many significant digits as the multiplied or divided measurement showing the least number of significant digits. Write the amount of sig figs above each number and then perform the mathematics 1) 13.3 x 2.7 = 7) 50.0 x 2.00 = 2) 21.3 x 3.58 = 8) 2.3 x 3.45 x 7.42 = 3) x 727 = 9) x = 4) 5003 / = 10) 51 / 7 = 5) 89 / 9.0 = 11) 208 / 9.0 = 6) 5121 / 55 = 12) / 5 =

10 Re-run 1) = 5) 6.77 x = 2) = 6) = 3) 2.15 x 3.11 x 121 = 7) / 82 = 4) 9634 / = = C. POWERS OF 10 AND SCIENTIFIC NOTATION Target 14 - Recall basic knowledge about powers of 10. Questions 1. Where is the decimal of all numbers if it is not written? 2. What does a power of ten tell you to do with the decimal? 3. Rewrite 10 x 10 x 10 with an exponent? Target 15 - Define scientific notation, identify its parts, and explain why it is important. A. Scientific notation method for writing very large and very small numbers so that they are easier to understand; shortcut for writing large and small numbers. B. Scientific notation always contains 3 parts. 1. Coefficient 2. Power of Exponent In each example, Label the coefficient, power of 10, and exponent Example 1 Example x x 10 7

11 C. One important rule about the coefficient It must be a number equal to or greater than 1 and less than ten. D. Scientific notation is the product of 2 numbers (2 numbers multiplied) E. Scientific notation is based on powers of ten. F. Scientific notation is important because it makes large and small numbers easier to understand. Questions 1. What is scientific notation? 2. What are the 3 parts of scientific notation? 3. Why is scientific notation important? 4. What is the one important rule about the coefficient? Target 16 - Convert large numbers back and forth between scientific notation and standard form. Put these numbers Put these numbers into in standard form scientific notation x x x x x Target 17 - Convert small numbers back and forth between scientific notation and standard form. Target 18 - Enter scientific notation into a calculator. A. Any scientific calculator will understand scientific notation if you use it correctly. B. When entering scientific notation into a calculator, you must type in 3 things. 1. Coefficient 2. Power of Exponent C. In order to do this, you must find a special button on your calculator. D. This button is called the power of 10 button. E. There are 2 common ways that calculators label this button. EE EXP F. Look for these buttons on your calculator. It should have one or the other, not both. G. Once you have found the power of 10 button, write the label here H. There are 3 steps 1. Type in the coefficient 2. Hit the power of 10 button 3. Type in the exponent I. Type this number into your calculator x 10 1

12 Target 19 - Multiply large and small numbers using scientific notation. Notes A. In order to multiply large numbers, you will need your calculator. B. This is best learned by doing Perform these exercises C. Coefficients will determine sig figs. 1 [6.84 x 10 3 ] x [4.54 x 10 6 ] 2 [2.0 x ] x [8.5 x 10 5 ] 3 [4.42 x 10-6 ] x [8.67 x 10-7 ] 4 [3.7 x 10 9 ] x [7.3 x 10-2 ] 5 [8.77 x ] x [3.714 x ] 6 [5.0 x 10-2 ] x [7.85 x ] 7 [1.042 x ] x [4.002 x ] Important There are other methods for performing this task on your calculator. In order to keep things simple, only one method will be taught. Most of the time, when students use other methods, they get wrong answers. You are strongly urged to use the method taught in class. Target 20 - Divide large and small numbers using scientific notation. 1 [2.21 x ] [1.44 x 10 3 ] 2 [1.92 x 10-2 ] [2.3 x 10 8 ] 3 [9.4 x 10 2 ] [1.24 x 10-9 ] 4 [9.2 x 10-3 ] [6.3 x ] 5 [2.4 x 10 6 ] [5.49 x 10-9 ] 6 [4.5 x 10 9 ] [2.45 x 10-4 ] 7 [3.6 x 10-6 ] [2.1 x ]

13 If your calculator is not working, here is how you do it by hand to save time, this will not be taught in class, but after school by request. Rule for Multiplication - When you multiply numbers with scientific notation, multiply the coefficients together and add the exponents. The base will remain 10. Rule for Division - When dividing with scientific notation, divide the coefficients and subtract the exponents. The base will remain 10. Part D Background Information about Conversions Target 21 - Define conversion A. Conversion - method where a measurement is rewritten using different units. B. For example If you measure the length of a cube to be 8.35 centimeters, you can calculate how many inches this would be this is a conversion (centimeters to inches) C. Using the ruler above, perform the following conversions English unit (inches) Metric unit (centimeters) English unit (inches) inch inches Metric unit (centimeters) inches inches inches inches Target 22 - Identify the different forms of conversions common in chemistry. A. There are 3 kinds of conversions that we will study 1. Metric to Metric 2. Metric to English (and in reverse) 3. SI to English (and in reverse) Target 23 Identify the various units common in the English System. A. Mass pounds, ounces B. Volume Gallons, quarts, pints, cups, tablespoons, fluid ounces, etc C. Energy Fahrenheit (temperature) D. Time seconds, minutes, hours

14 Target 24 Explain how the Metric system is organized with units. Metric system *This chart can be expressed with reverse exponents depending on the mathematical point of view Giga Mega Kilo Hecto Deca Base Deci Centi Milli Micro nano G M k h da Gram Liter Joule Meter d c m µ n A. The base units represent measurements counting in the ones place. B. Prefixes of the base units will determine to which decimal place value is being expressed. C. What is a prefix? 1. A prefix is a description that comes before a metric base unit. 2. For example centimeters centi is the prefix for the base unit meter 3. Centi means one hundredth 4. Therefore, 1 centimeter is 1 hundredth of a meter (remember that 1 cent is one hundredth of dollar.) D. Common metric prefixes include kilo, centi, milli, others E. Here are some metric base units that we will study in chemistry 1. Mass - grams 2. Volume - Liters 3. Energy Celsius, Calories, Joules, Kelvins (all measurements of energy) 4. Time seconds Target 25 Compare the metric system and the English system. A. Compare explain how 2 things are similar and different. Venn Diagram

15 Target 26 Identify abbreviations for measurements common in chemistry. Mass Abbrev Volume Abbrev Energy Abbrev Time Pound Gallon Joule Hour Abbrev Ounce Fluid Calorie Minute Ounce Gram Liter Fahrenheit Second Kilogram Kiloliter Celsius millisecond Milligram Milliliter Kelvin microsecond Part E Calculations and Conversions Target 27 - Perform unit conversions within the metric system Thumb rule Giga Mega Kilo Hecto Deca Base Deci Centi Milli Micro nano G M k h da d c m µ n Giga Mega Kilo Hecto Deca Base Deci Centi Milli Micro nano G M k h da d c m µ n A. Mass 1. What is the metric base for measuring mass? 2. What is mass a measure of? kg µg g g dag dg mg kg mg kg mg kg mg kg g µg

16 kg kg mg mg g Mg Questions 1. How many grams are in 1 kilogram? 2. How many milligrams are in 1 gram? 3. How many milligrams are in 1 kilogram? 4. Name an object that weighs about 1 gram. 5. Name an object that weighs about 1000 milligrams. 6. Name an object that weighs about 1 kilogram. g mg B. Volume What is the metric base unit for measuring volume? What is volume a measure of? Liters dl ml ml ml ml kl L ML hl L L GL L 5. 5 kl kl kl kl ml ml ml ml kl µl Questions 1. How many liters are in 1 Kiloliter? 2. How many milliliters are in 1 liter? 3. Name an object that has a volume of about 1 liter. 4. Name an object that has a volume of about 1 milliliter. 5. Name an object that has a volume of about 1 kiloliter. All together now mg kl g dal

17 L kg kl ml L hg Gg ml µl µl g mg µg ml L mg kg mg µl Mg Questions 1. The mass of a potato is measured in. 2. The amount of water in a beaker is measured in. 3. The length of a table is measured in. 4. A 2.0 liter bottle of Mountain Dew is how many ml? 5. A 5.0 gram vitamin pill is how many milligrams? Targets Skipped for now Target 31 - Convert various units of temperature English, metric, and SI A. Celsius and Fahrenheit (ºF 32) x.56 = ºC (ºC x 1.8) + 32 = ºF Notes Perform the conversions 1 Convert 77.1 ºC to ºF 6 Convert ºCelsius to ºFahrenheit 2 Convert 58.6 ºC to ºF 7 Convert 55.0 ºFahrenheit to ºCelsius

18 3 Convert 11.0 ºF to ºC 8 Convert ºCelsius to ºFahrenheit 4 Convert ºF to ºC 9 Convert 2.6 x 10 2 ºF to C 5 Convert 97.6 ºF to ºC 10 Convert 0.11 ºC to º F B. Celsius and Kelvin K = ºC ºC = K a. Convert degrees Celsius to Kelvins - add 273 to the Celsius temperature. Example - Convert 44 ºC to Kelvins = 317 K (Kelvins) b. Convert Kelvins to degrees Celsius subtract 273 from the Kelvin temperature Example Convert 434 Kelvins (K) to degrees Celsius = 161 ºC Perform the conversions 1 Convert 45.1 ºC to Kelvins 6 Convert 62.5 ºC to K 2 Convert 22.6 ºC to Kelvins 7 Convert K to ºC 3 Convert Kelvins to ºC 8 Convert ºC to K 4 Convert 97.2 Kelvins to ºC 9 Convert 2.6 x 10 2 ºC to K 5 Convert 77.2 Kelvins to ºC 10 Convert 0.0 K to º C Target 32 Define Absolute Zero and explain how the Kelvin Temperature scale was developed. A. Each winter, some parts of the world experience cold weather. B. Water freezes, it snows, and people must wear more clothing in order to remain warm. C. Humans usually consider 0 ºC to be a cold temperature. (this is the freezing point of water) D. How much colder can it get? Is there a lowest temperature? E. Yes, there is a lowest temperature it is called ABSOLUTE ZERO. F. Absolute Zero is -273 ºC (it can t get any colder than this) G. Scientists decided to create a new temperature measurement system that did not have any negative numbers. H. They decided that absolute zero would be the bottom and set -273 º C as zero Kelvins. I. In other words, the Kelvin temperature scale has no negative numbers. This becomes useful in chemistry. J. Absolute zero = zero Kelvins (0 K). K. Therefore, in order to convert Celsius to Kelvins, you simply add 273. to the Celsius temperature Questions 1. What is the coldest temperature using the Celsius Scale? 2. What is the coldest temperature using the Kelvin Scale? 3. How do you convert Celsius to Kelvin? 4. How do you convert Kelvin to Celsius? 5. Why is is the Kelvin scale useful in chemistry?

19 PART F - DENSITY Target 33 - Describe/define density. A. There are several ways of describing density 1. Density is the relationship between an object s mass and 2. Density can be calculated by dividing an object s mass by its volume. D = M / V or Density = Mass / Volume 3. Density will have units mass and volume. a. For example, the density of quartz is grams/milliliters 4. Any sample size of the same substance will have the same. a. Example: a liter of water will have the same density as a swimming pool of water. 5. Density can also be a description of how a sample of matter is. 6. A substance of lesser density will always float on a substance of greater density. a. Example: oil floats in water therefore, oil is less dense than water. Target 34 - Explain density as a measure of Compactness (Page 90) A. What is meant by compact? B. Remember that is anything made of atoms. C. Atoms can be squeezed together to occupy less space (less volume). D. When the volume of matter is squeezed together, it is more compact. 1. Example You can squeeze a pillow to a smaller volume the squeezed pillow would be considered more compact than a pillow left unbothered. However, the squeezed pillow would have the as the unbothered pillow. Therefore the compact pillow is more dense. 2. More compact = more dense. 3. If atoms are closer together, they occupy less space (more compact) Questions 1. What can you say about atoms that are squeezed together? 2. What is meant by the term compact? 3. Allyson Tyra squeezes a sponge and it becomes smaller. What can be said about the density of the sponge after she squeezed it? 4. How many units will a measurement of density have? Target 35 - Calculate the volume of various forms of matter including solid shapes cube, sphere, irregular - using the metric system. A. Calculating the volume of a liquid is easy, just pour the liquid in a graduated cylinder and read the graduations. B. Calculating the volume of a solid is more challenging; you have to know the dimensions. C. We will measure (calculate) the volume of 3 shapes. 1. Cube/rectangular box 2. Sphere 3. Irregular

20 Calculate the volume of a rectangle or cube. Formula -- - Volume = L x W x H Length =4.05 cm Width = 3.75 cm Height=3.50 cm Calculate the volume of a sphere. Formula --- Volume = 4/3πr 3 Radius = 2.25cm Measure the volume of an irregular shape Notes Target 36 - Explain the relationship between milliliters and cubic centimeters (page 89) 1 milliliter = 1 cubic centimeter OR 1 ml = 1cm 3 Notes Questions: 1. How many cubic centimeters is 10 milliliters? 2. How many cubic centimeters is milliliters? 3. How many milliliters is 34 cubic centimeters? 4. How many milliliters is 88.9 cubic centimeters? 5. What is the abbreviation for cubic centimeters? 6. What is the abbreviation for milliliters? 7. How many cm 3 is 37 ml? 8. How many ml is cm 3?

21 Target 37 - Solve single variable algebraic equations Notes Target 38 - Calculate density (Page 90) A. Calculating density requires the following equation D = M / V or Density = Mass / Volume B. Just like in Algebra, you replace letters with appropriate numbers. C. Whenever you are asked to calculate density, you will be given mass and volume. Notes Examples; 1. Zach Busse has a cube with a mass of 244 grams and a volume of 103 milliliters. What is the density of the cube? 2. Laura Kaufman has a rock with a mass of grams and a volume of milliliters. What is the density of the cookie dough? 3. Caleb Hale has a ball of cookie dough with a mass of 25 grams and a volume of 75 milliliters. What is the density of the rock? 4. Place the objects in order from lowest density to highest density. Low Medium High

22 Target 39 - Calculate volume (Page 92) A. When calculating the volume of an object, you must know the density and the mass. B. Calculating Volume uses the same equation as used above. Notes Examples 1. Nicole Ferrara has a marble with a density of 2.61 grams per milliliter (g/ml) and a mass of 101 grams. What is the volume of the marble? 2. David Jones has a basketball with a density of.896 g/ml and a mass of 241 grams. What is the volume? 3. Brittany Moeckel has a steel bowling ball with a density of 7.81 g/ml and a mass of 802 grams. What is the volume of the ball? 4. Place the objects in order from lowest volume to highest volume. Low Medium High Target 40 - Calculate mass (Page 92) A. When calculating the Mass of an object, you must know the density and the volume. B. Calculating Mass uses the same equation as used above. Notes Examples 1. Audra Johnson has a brass statue with a density of 8.40 g/ml and a volume of 69 milliliters. What is the mass? 2. Ryan Smith has a quartz crystal with a density of 4.31 g/ml and a volume of 209 milliliters. What is the mass? 3. Taylor Johnson has ball of modeling clay with a density of 1.67 g/ml and a volume of 562 milliliters. What is the mass? 4. Place the objects in order from lowest mass to highest mass. Low Medium High

23 Complete the table mind your sig figs Substance Mass (grams) Volume (milliliters) Density (g/ml) Gold.301mL 19.3 g/ml Table sugar.960g 1.59 g/ml Gasoline 3.22g 4.29mL Target 41 - Explain density as a relationship between volume and particle spacing. Models of density the cube Target 42 - Explain how objects of different sizes can have the same mass (Page 89) Calculate the density for each cube. Questions 1. Calculate the density for each cube write your answers in the table above. 2. How can the objects above have the same mass if they are different sizes? 3. Genius question - Convert the volume of each substance above to milliliters. Lithium ml Water ml Lead ml

24 Target 43 - Explain how objects of the same size can have different masses. A. Objects of the same size can have different masses because of particle spacing when the spaces between particles are small, more particles can fit. B. Which cube is more dense? How do you know? Target 44 - Calculate the density of substances and predict which substances will float on which. A. Remember from earlier that a substance of lesser density will always float on a substance of greater density. B. Example: oil floats in water oil is less dense than water. Example 1 - Predict which substance will float on which. Mass (grams) Volume (milliliters) Density (g/ml) Substance A 25.0 g 50.0 ml Substance B 50.0 g 25.0 ml Which will float on which? Mass (grams) Volume (milliliters) Density (g/ml) Substance C g ml Substance D g ml Substance E g ml Which will float on which?