1. Chapter 1: Scientists’ Tools

2. Introductory Activity Think about the following questions:  What does “doing science” mean to you?  Who “does science”?  What do “scientists” do?  What do you think of when you hear about science or scientists?  What comes to mind when you hear about “chemistry” or “chemists”?  Do you think science plays an important role in your life? If yes, where do you see science in your world? If no, explain why not. Share your answers with a partner Share your answers as a class.

3. Chemistry is an Experimental Science This chapter will introduce the following tools that scientists use to “do chemistry”  Section 1.1: Scientific Processes  Section 1.2: Observations & Measurements  Section 1.3: Designing Labs  Section 1.4: Converting Units  Section 1.5: Significant digits  Section 1.6: Scientific Notation

4. Chemistry is an Experimental Science Common characteristics Although no one method, there are Careful observation s Accurate & precise measurements Design your own labs Unit conversions Significant digit rules Scientific Notation Are used when you include May require When using in calculations, follow May require using

5. Section 1.1—Doing Science

6. There is no “The Scientific Method” There is no 1 scientific method with “X” number of steps There are common processes that scientists use  Questioning & Observing  Gathering Data Experimentation Field Studies Long-term observations Surveys Literature reviews & more  Analyzing all the data  Using evidence & logic to draw conclusions  Communicating findings

7. Science is “loopy” Science is not a linear process…rather it is “loopy”…and it’s not just about experimentation …there are many pathways…even more than are shown here! Observations Questions Data gathering (experiment, literature research, field observations, long-term studies, etc.) Hypothesis Trend and pattern recognition Conclusion formation Communication & Validation Model Formation Product or technology formation

8. Two types of Experiments This text will predominantly use experimentation for data gathering Two types of experiments will be used:  To investigate relationships or effect How does volume affect pressure? How does reaction rate change with temperature?  To determine a specific value What is the value of the gas law constant? What is the concentration of that salt solution?

9. Variables Dependent VariableIndependent Variable Controlled by you You measure or observe Example: How does reaction rate change with temperatur e depends on

10. Variables Dependent VariableIndependent Variable Controlled by you You measure or observe Example: How does reaction rate change with temperatur e TemperatureReaction rate depends on

11. Variables Dependent VariableIndependent Variable Example: What is the concentratio n of that salt solution?

12. Variables Variables are not appropriate in specific value experiments Dependent VariableIndependent Variable Example: What is the concentratio n of that salt solution? Not appropriate

13. Constants It’s important to hold all variables other than the independent and dependent constant so that you can determine what actually caused the change! Constants Example: How does reaction rate change with temperatur e

14. Constants It’s important to hold all variables other than the independent and dependent constant so that you can determine what actually caused the change! Constants Concentrations of reactants Example: How does reaction rate change with temperatur e Volumes of reactants Method of determining rate of reaction And maybe you thought of some others!

15. Prediction versus Hypothesis They are different! HypothesisPrediction Just predicts Attempts to explain why you made that prediction Example: How does surface area affect reaction rate?

16. Prediction versus Hypothesis They are different! HypothesisPrediction Just predicts Attempts to explain why you made that prediction Example: How does surface area affect reaction rate? Reaction rate will increase as surface area increases Reaction rate will increase with surface area because more molecules can have successful collisions at the same time if more can come in contact with each other.

17. Predictions versus Hypothesis HypothesisPrediction Example: What is the concentratio n of that salt solution?

18. Predictions versus Hypothesis It is not appropriate to make a hypothesis or prediction in specific value experiments HypothesisPrediction Example: What is the concentratio n of that salt solution? Not appropriate—it would just be a random guess

19. Gathering Data Multiple trials help ensure that you’re results weren’t a one-time fluke! Precise—getting consistent data within experimental error Accurate—getting the “correct” or “accepted” answer consistently Example: Describe each group’s data as not precise, precise or accurate Correct value

20. Precise & Accurate Data Example: Describe each group’s data as not precise, precise or accurate Correct value Precise, but not accurate Precise & Accurate Not precise

21. Can you be accurate without precise? Correct value This group had one value that was almost right on…but can we say they were accurate?

22. Can you be accurate without precise? Correct value This group had one value that was almost right on…but can we say they were accurate? No…they weren’t consistently correct. It was by random chance that they had a result close to the correct answer.

23. Precise is consistent within experimental error. What does that mean? Every measurement has some error in it…we can’t measure things perfectly. You won’t get exactly identical results each time. “Within Experimental Error” Correct value You have to decide if the variance in your results is within acceptable experimental error

24. Scientists take into account all the evidence from the data gathering and draw logical conclusions Conclusions can support or not support earlier hypothesis Conclusions can lead to new hypothesis, which can lead to new investigations As evidence builds for conclusions, theories and laws can be formed. Drawing Conclusions

25. Theory versus Law Many people do not understand the difference between these two terms LawTheory Describes why something occurs Describes or predicts what happens (often mathematical) Example: The relationship between pressure and volume Cannot ever become

26. Theory versus Law Many people do not understand the difference between these two terms LawTheory Describes why something occurs Describes or predicts what happens (often mathematical) Example: The relationship between pressure and volume Kinetic Molecular Theory— as volume decreases, the frequency of collisions with the wall will increase & the collisions are the “pressure” Boyle’s Law: P 1 V 1 = P 2 V 2 Cannot ever become

27. Scientists share results with the scientific community to:  Validate findings (see if others have similar results)  Add to the pool of knowledge Scientists use many ways to do this:  Presentations and posters at conference  Articles in journals  Online collaboration & discussions  Collaboration between separate groups working on similar problems Communicating Results

28. Section 1.2—Observations & Measurements

29. Taking Observations Qualitative descriptions  Color  Texture  Formation of solids, liquids, gases  Heat changes  Anything else you observe

30. Clear versus Colorless Clear See-through Cloudy Parts are see- through with solid “cloud” in it Opaque Cannot be seen through at all Words to describe transparency Colorless does not describe transparency  You can be clear & colored  You need to describe the color of the solution & the cloud if it’s cloudy (examples: blue solution & white cloud or colorless solution and blue solid)

31. Clear versus Colorless Cherry Kool-ade Example: Describe the following in terms of transparency words & colors Whole Milk Water

32. Clear versus Colorless Cherry Kool-adeClear & red Example: Describe the following in terms of transparency words & colors Whole Milk Water Opaque & white Clear & Colorless

33. Gathering Data Quantitative measurements International System of Units (SI Units) are used Quantity Mass (how much stuff is there) Unit Kilogram (kg) Instrument used Balance Volume (how much space it takes up) Liters (L) Graduated cylinder Temperature (how fast the particles are moving) Kelvin (K) or Celsius (°C) Thermometer Length Meters (m) Meter stick Time Seconds (sec) stopwatch Energy Joules (J) (Measured indirectly)

34. Uncertainty in Measurement Every measurement has a degree of uncertainty The last decimal you write down is an estimate  Write down a “5” if it’s in-between lines  Write down a “0” if it’s on the line 5 mL 10 15 20 25 mL 5 mL 10 15 20 25 mL Remember: Always read liquid levels from the bottom of the meniscus (the bubble at the top) Example: Read the measurements

35. Uncertainty in Measurement Every measurement has a degree of uncertainty The last decimal you write down is an estimate  Write down a “5” if it’s in-between lines  Write down a “0” if it’s on the line 5 mL 10 15 20 25 mL 5 mL 10 15 20 25 mL Example: Read the measurements It’s in- between the 10 & 11 line 10.5 mL It’s on the 12 line 12.0 mL

36. Uncertainty in Measurement Example: Read the measurements 1234567812345678

37. Uncertainty in Measurement Example: Read the measurements 1234567812345678 It’s right on the 4.3 line 4.30 It’s between the 3.8 & 3.9 line 3.85

38. Uncertainty in Measurement Choose the right instrument  If you need to measure out 5 mL, don’t choose the graduated cylinder that can hold 100 mL. Use the 10 or 25 mL cylinder The smaller the measurement, the more an error matters—use extra caution with small quantities  If you’re measuring 5 mL & you’re off by 1 mL, that’s a 20% error  If you’re measuring 100 mL & you’re off by 1 mL, that’s only a 1% error

39. Section 1.3—Designing Your Own Labs

40. Designing Labs This is not giving a “scientific method”…rather it’s giving hints at how to stay focused on the goal when designing a lab to allow you to write them more efficiently It gives you a plan of attack, but you can adjust it as you need for various labs

41. Identify the purpose, problem, question If variables are appropriate (relationship or effect lab), identify them in the problem  Example of a purpose: To determine the effect of temperature on pressure If variables are not appropriate, be as descriptive as possible  Example of a question: What is the concentration of a saturated NaCl solution at room temperature? You can phrase it as a purpose or question You should also identify any important constants

42. Gather Background Information The background information section is where you put together all the different concepts you know together to solve your problem or answer your question It might contain:  Definitions  Known relationships  Equations

43. Write a hypothesis Only when appropriate—only in relationship or effect labs After looking at all your background information, make a hypothesis (prediction with explanation for why you think so)

44. Set-up the Results/Calculations section Write any equations that you will need to solve your problem or answer your questions. You won’t have numbers to plug in, but you can set up the equations/calculations now.

45. Set-up the Data Table Go through the calculations you set up and make a data table that asks for each quantity you’ll need Remember that some measurements must be taken indirectly & you will need to take that into account:  For example, you can’t put a chemical directly on the balance, so you’ll need the mass of the container (beaker or weighing dish) and then the mass of the container & chemical in your data table Your data table should not contain any calculated values (even just subtracting out the mass of the beaker)…only those you will actually measure with an instrument!

46. Write your Procedure Procedures should be:  Clear, Concise, Numbered list of steps  Repeatable by someone of your same level of experience/education Go through your data table and write a procedure step to measure each thing asked for in your data table. If the data table includes masses or volumes of chemicals, give an approximate amount in the procedure  Example: Add approximately 2 g of NaCl to the beaker. Find exact mass & record.

47. Write your Materials List Go through your procedure and make a list of each piece of equipment and chemical that you’ll need Be sure to include how many of each type of equipment and what approximate quantity of chemical  You don’t need to specify the amount of water needed!

48. Write your Safety Concerns Go through your procedure & materials list and specify any safety concerns. Possibilities include:  Wear goggles (anytime you use glass or chemicals)  Use caution with glassware  Use caution with hot glassware or hot chemicals  Any cautions specific to a chemical you’re using (your teacher will tell you these)  Report any spills, breaks or incidents to your teacher immediately  Wear aprons or gloves, if necessary

49. Now you’re ready to do your lab! Begin performing your lab (after your teacher checks it for safety, if necessary) If you need to make changes to your procedure at any time (you realize it’s not quite right)…that’s OK  Just make sure you change the written procedure as well so that when you’re done, the written report reflects what you actually did Record your data in the data table Complete the calculations you’ve set up

50. Write your Conclusion Restate the purpose Completely answer the purpose with your results Address any earlier hypothesis…does your evidence support or not support it?  If it does not support the hypothesis, propose a new hypothesis Suggest possible sources of error  “human error” is not specific enough & “Calculations” doesn’t count

51. Section 1.4—Converting Units

52. Converting Units Often, a measurement is more convenient in one unit but is needed in another unit for calculations. Dimensional Analysis is a method for converting unit You may have learned another method of converting units in math or previous science classes…trust me…learn this one now! It will help you solve many other chemistry problems later in the class!

53. Equivalents Dimensional Analysis uses equivalents…what are they? 1 foot = 12 inches What happens if you put one on top of the other? 1 foot 12 inches

54. Equivalents Dimensional Analysis uses equivalents…what are they? 1 foot = 12 inches What happens if you put one on top of the other? 1 foot 12 inches When you put two things that are equal on top & on bottom, they cancel out and equal 1 = 1

55. Dimensional Analysis Dimensional analysis is based on the idea that you can multiply anything by 1 as many times as you want and you won’t change the physical meaning of the measurement! 27 inches 1  = 27 inches

56. Dimensional Analysis Dimensional analysis is based on the idea that you can multiply anything by 1 as many times as you want and you won’t change the physical meaning of the measurement! 1 foot 12 inches = 2.25 feet 27 inches  1  = 27 inches

57. Dimensional Analysis Dimensional analysis is based on the idea that you can multiply anything by 1 as many times as you want and you won’t change the physical meaning of the measurement! 1 foot 12 inches = 2.25 feet 27 inches  Remember…this equals “1” 27 inches 1  = 27 inches Same physical meaning…it’s the same length either way!

58. 1 foot 12 inches  Canceling Anything that is on the top and the bottom of an expression will cancel When canceling units…just cancel the units… 1 foot 12 inches 27 inches  Unless the numbers cancel as well!

59. Steps for using Dimensional Analysis 1 Write down your given information 2 Write down an answer blank and the desired unit on the right side of the problem space 3 Use equivalents to cancel unwanted unit and get desired unit. 4 Calculate the answer…multiply across the top & divide across the bottom of the expression

60. Common Equivalents 1 ft 12 in 1 in 2.54 cm 1 min 60 s 1 hr 3600 s 1 quart (qt) 0.946 L 4 pints 1 quart 1 pound (lb) 454 g = = = = = = =

61. Example #1 Example: How many grams are equal to 1.25 pounds? 1.25 lb 1 Write down your given information

62. Example #1 Example: How many grams are equal to 1.25 pounds? 1.25 lb 2 Write down an answer blank and the desired unit on the right side of the problem space = ________ g

63. Example #1 Example: How many grams are equal to 1.25 pounds? 1.25 lb = ________ g 3 Use equivalents to cancel unwanted unit and get desired unit. The equivalent with these 2 units is: 1 lb = 454 g A tip is to arrange the units first and then fill in numbers later!  lb g Put the unit on bottom that you want to cancel out! 1 454

64. Example #1 Example: How many grams are equal to 1.25 pounds? 1.25 lb = ________ g  lb g 1 454 4 Calculate the answer…multiply across the top & divide across the bottom of the expression Enter into the calculator: 1.25  454  1 568

65. Metric Prefixes Metric prefixes can be used to form equivalents as well First, you must know the common metric prefixes used in chemistry kilo- (k) 1000 deci- (d) 0.1 centi- (c) 0.01 milli- (m) 0.001 micro- ( μ) 0.000001 nano (n) 0.000000001 = = = = = = These prefixes work with any base unit, such as grams (g), liters (L), meters (m), seconds (s), etc.

66. Metric Equivalents Many students confuse where to put the number shown in the previous chart…it always goes with the base unit (the one without a prefix) kilo = 1000 There are two options: 1 kg = 1000 g 1000 kg = 1 g Example: Write a correct equivalent between “kg” and “g” To help you write correct equivalents, read the number that equals the prefix as the prefix itself in a “sentence”

67. Metric Equivalents Many students confuse where to put the number shown in the previous chart…it always goes with the base unit (the one without a prefix) kilo = 1000 There are two options: 1 kg = 1000 g 1000 kg = 1 g Example: Write a correct equivalent between “kg” and “g” “1 kg is kilo-gram”…correct “kilo- kg is 1 gram”…incorrect To help you write correct equivalents, read the number that equals the prefix as the prefix itself in a “sentence”

68. Try More Metric Equivalents milli = 0.001 There are two options: 1 L = 0.001 mL 0.001 L = 1 mL Example: Write a correct equivalent between “mL” and “L” centi = 0.01 There are two options: 1 cm = 0.01 m 0.01 cm = 1 m Example: Write a correct equivalent between “cm” and “m”

69. Try More Metric Equivalents milli = 0.001 There are two options: 1 L = 0.001 mL 0.001 L = 1 mL Example: Write a correct equivalent between “mL” and “L” “1 L is milli-mL”…incorrect “milli-liter is 1 mL”…correct centi = 0.01 There are two options: 1 cm = 0.01 m 0.01 cm = 1 m Example: Write a correct equivalent between “cm” and “m” “1 cm is centi-meter”…correct “centi-cm is 1 m”…incorrect

70. Metric Volume Units To find the volume of a cube, measure each side and calculate: length  width  height length height width But most chemicals aren’t nice, neat cubes! Therefore, they defined 1 milliliter as equal to 1 cm 3 (the volume of a cube with 1 cm as each side measurement) 1 cm 3 1 mL =

71. Example #2 Example: How many grams are equal to 127.0 mg? 127.0 mg = ________ g You want to convert between mg & g “1 mg is 1 milli-g” 1 mg = 0.001 g

72. Example #2 Example: How many grams are equal to 127.0 mg? 127.0 mg = ________ g  mg g 1 0.001 Enter into the calculator: 127.0  0.001  1 0.1270 You want to convert between mg & g “1 mg is 1 milli-g” 1 mg = 0.001 g You may be able to do this in your head…but practice the technique on the more simple problems so that you’ll be a dimensional analysis pro for the more difficult problems (like stoichiometry)!

73. Multi-step problems There isn’t always an equivalent that goes directly from where you are to where you want to go! Rather than trying to determine a new equivalent, it’s faster to use more than one step in dimensional analysis! This way you have fewer equivalents to remember and you’ll make mistakes more often With multi-step problems, it’s often best to plug in units first, then go back and do numbers.

74. Example #3 Example: How many kilograms are equal to 345 cg? 345 cg = _______ kg There is no equivalent between cg & kg With metric units, you can always get to the base unit from any prefix! And you can always get to any prefix from the base unit! You can go from “cg” to “g” Then you can go from “g” to “kg”

75. 345 cg = _______ kg Example #3 Example: How many kilograms are equal to 345 cg?  cg g Go to the base unit  g kg Go from the base unit

76. = _______ kg Example #3 Example: How many kilograms are equal to 345 cg?  cg g 1 0.01 345 cg  g kg 1000 1 1 cg = 0.01 g 1000 g = 1 kg Remember—the # goes with the base unit & the “1” with the prefix!

77. = _______ kg Example #3 Example: How many kilograms are equal to 345 cg?  cg g 1 0.01 Enter into the calculator: 345  0.01  1  1  1000 0.00345 345 cg  g kg 1000 1 Whenever dividing by more than 1 number, hit the divide key before EACH number! It doesn’t matter what order you type this in…you could multiply, divide, multiply divide if you wanted to!

78. Let’s Practice #1 Example: 0.250 kg is equal to how many grams?

79. 1000 0.250 kg Let’s Practice #1 Example: 0.250 kg is equal to how many grams? = ______ g  kg g 1 1 kg = 1000 g Enter into the calculator: 0.250  1000  1 250.

80. Let’s Practice #2 Example: How many mL is equal to 2.78 L?

81. 1 2.78 L Let’s Practice #2 Example: How many mL is equal to 2.78 L? = ______ mL  L mL.001 1 mL = 0.001 L Enter into the calculator: 2.78  1  0.001 2780

82. Let’s Practice #3 Example: 147 cm 3 is equal to how many liters?

83. Let’s Practice #3 Example: 147 cm 3 is equal to how many liters? Remember—cm 3 is a volume unit, not a length like meters! = _______ L  cm 3 mL 1 1 147 cm 3  mL L 1 0.001 There isn’t one direct equivalent 1 cm 3 = 1 mL 1 mL = 0.001 L Enter into the calculator: 147  1  0.001  1  1 0.147

84. Let’s Practice #4 Example: How many milligrams are equal to 0.275 kg?

85. Let’s Practice #4 Example: How many milligrams are equal to 0.275 kg? = _______ mg  kg g 1 1000 0.275 kg  g mg 0.001 1 There isn’t one direct equivalent 1 kg = 1000 g 1 mg = 0.001 g Enter into the calculator: 0.275  1000  1  1  0.001 275,000

86. Section 1.5—Significant Digits

87. Section 1.5 A Counting significant digits

88. Taking & Using Measurements You learned in Section 1.3 how to take careful measurements Most of the time, you will need to complete calculations with those measurements to understand your results 1.00 g 3.0 mL = 0.3333333333333333333 g/mL If the actual measurements were only taken to 1 or 2 decimal places… how can the answer be known to and infinite number of decimal places? It can’t!

89. Significant Digits A significant digit is anything that you measured in the lab—it has physical meaning The real purpose of “significant digits” is to know how many places to record in an answer from a calculation But before we can do this, we need to learn how to count significant digits in a measurement

90. Significant Digit Rules 1 All measured numbers are significant 2 All non-zero numbers are significant 3 Middle zeros are always significant 4 Trailing zeros are significant if there’s a decimal place 5 Leading zeros are never significant

91. All the fuss about zeros 102.5 g Middle zeros are important…we know that’s a zero (as opposed to being 112.5)…it was measured to be a zero 125.0 mL The convention is that if there are ending zeros with a decimal place, the zeros were measured and it’s indicating how precise the measurement was. 125.0 is between 124.9 and 125.1 125 is between 124 and 126 0.0127 m The leading zeros will dissapear if the units are changed without affecting the physical meaning or precision…therefore they are not significant 0.0127 m is the same as 127 mm

92. Sum it up into 2 Rules 1 If there is no decimal point in the number, count from the first non-zero number to the last non-zero number 2 If there is a decimal point (anywhere in the number), count from the first non-zero number to the very end The 4 earlier rules can be summed up into 2 general rules

93. Examples of Summary Rule 1 Example: Count the number of significant figures in each number 124 20570 200 150 1 If there is no decimal point in the number, count from the first non-zero number to the last non-zero number

94. Examples of Summary Rule 1 Example: Count the number of significant figures in each number 124 20570 200 150 1 If there is no decimal point in the number, count from the first non-zero number to the last non-zero number 3 significant digits 4 significant digits 1 significant digit 2 significant digits

95. Examples of Summary Rule 2 Example: Count the number of significant figures in each number 0.00240 240. 370.0 0.02020 2 If there is a decimal point (anywhere in the number), count from the first non-zero number to the very end

96. Examples of Summary Rule 2 Example: Count the number of significant figures in each number 0.00240 240. 370.0 0.02020 3 significant digits 4 significant digits 2 If there is a decimal point (anywhere in the number), count from the first non-zero number to the very end

97. Importance of Trailing Zeros Just because the zero isn’t “significant” doesn’t mean it’s not important and you don’t have to write it! “250 m” is not the same thing as “25 m” just because the zero isn’t significant The zero not being significant just tells us that it’s a broader range…the real value of “250 m” is between 240 m & 260 m. “250. m” with the zero being significant tells us the range is from 249 m to 251 m

98. Let’s Practice Example: Count the number of significant figures in each number 1020 m 0.00205 g 100.0 m 10240 mL 10.320 g

99. Let’s Practice Example: Count the number of significant figures in each number 1020 m 0.00205 g 100.0 m 10240 mL 10.320 g 3 significant digits 4 significant digits 5 significant digits

100. Section 1.5 B Calculations with significant digits

101. Performing Calculations with Sig Digs 1 Addition & Subtraction: Answer has least number of decimal places as appears in the problem 2 Multiplication & Division: Answer has least number of significant figures as appears in the problem When recording a calculated answer, you can only be as precise as your least precise measurement Always complete the calculations first, and then round at the end!

102. Addition & Subtraction Example #1 Example: Compute & write the answer with the correct number of sig digs 15.502 g + 1.25 g This answer assumes the missing digit in the problem is a zero…but we really don’t have any idea what it is 1 Addition & Subtraction: Answer has least number of decimal places as appears in the problem 16.752 g

103. Addition & Subtraction Example #1 Example: Compute & write the answer with the correct number of sig digs 15.502 g + 1.25 g 1 Addition & Subtraction: Answer has least number of decimal places as appears in the problem 16.752 g 16.75 g 3 decimal places 2 decimal places Lowest is “2” Answer is rounded to 2 decimal places

104. Addition & Subtraction Example #2 Example: Compute & write the answer with the correct number of sig digs 10.25 mL - 2.242 mL This answer assumes the missing digit in the problem is a zero…but we really don’t have any idea what it is 1 Addition & Subtraction: Answer has least number of decimal places as appears in the problem 8.008 mL

105. Addition & Subtraction Example #2 Example: Compute & write the answer with the correct number of sig digs 10.25 mL - 2.242 mL 1 Addition & Subtraction: Answer has least number of decimal places as appears in the problem 8.01 mL 2 decimal places 3 decimal places Lowest is “2” Answer is rounded to 2 decimal places 8.008 mL

106. Multiplication & Division Example #1 Example: Compute & write the answer with the correct number of sig digs 10.25 g 2.7 mL = 3.796296296 g/mL 2 Multiplication & Division: Answer has least number of significant figures as appears in the problem

107. Multiplication & Division Example #1 Example: Compute & write the answer with the correct number of sig digs 3.8 g/mL 4 significant digits 2 significant digits Lowest is “2” Answer is rounded to 2 sig digs 10.25 g 2.7 mL = 3.796296296 g/mL 2 Multiplication & Division: Answer has least number of significant figures as appears in the problem

108. Multiplication & Division Example #2 Example: Compute & write the answer with the correct number of sig digs 1.704 g/mL  2.75 mL 4.686 g 2 Multiplication & Division: Answer has least number of significant figures as appears in the problem

109. Multiplication & Division Example #2 Example: Compute & write the answer with the correct number of sig digs 4.69 g 4 significant dig 3 significant dig Lowest is “3” Answer is rounded to 3 significant digits 2 Multiplication & Division: Answer has least number of significant figures as appears in the problem 1.704 g/mL  2.75 mL 4.686 g

110. Let’s Practice #1 Example: Compute & write the answer with the correct number of sig digs 0.045 g + 1.2 g

111. Let’s Practice #1 Example: Compute & write the answer with the correct number of sig digs 1.2 g 3 decimal places 1 decimal place Lowest is “1” Answer is rounded to 1 decimal place 1.245 g Addition & Subtraction use number of decimal places! 0.045 g + 1.2 g

112. Let’s Practice #2 Example: Compute & write the answer with the correct number of sig digs 2.5 g/mL  23.5 mL

113. Let’s Practice #2 Example: Compute & write the answer with the correct number of sig digs 59 g 2 significant dig 3 significant dig Lowest is “2” Answer is rounded to 2 significant digits 2.5 g/mL  23.5 mL 58.75 g Multiplication & Division use number of significant digits!

114. Let’s Practice #3 Example: Compute & write the answer with the correct number of sig digs 1.000 g 2.34 mL

115. Let’s Practice #3 Example: Compute & write the answer with the correct number of sig digs 0.427 g/mL 4 significant digits 3 significant digits Lowest is “3” Answer is rounded to 3 sig digs 1.000 g 2.34 mL = 0.42735 g/mL Multiplication & Division use number of significant digits!

116. Section 1.6—Scientific Notation

117. Scientific Notation Scientific Notation is a form of writing very large or very small numbers that you’ve probably used in science or math class before Scientific notation uses powers of 10 to shorten the writing of a number.

118. Writing in Scientific Notation The decimal point is put behind the first non-zero number The power of 10 is the number of times it moved to get there A number that began large (>1) has a positive exponent & a number that began small (<1) has a negative exponent

119. Example #1 Example: Write the following numbers in scientific notation. 12457.656 m 0.000065423 g 128.90 g 0.0000007532 m

120. Example #1 Example: Write the following numbers in scientific notation. 12457.656 m 0.000065423 g 128.90 g 0.0000007532 m 1.24567656  10 m 4 6.5423  10 g -5 1.2890  10 m 2 7.532  10 m -7 The decimal is moved to follow the first non-zero number The power of 10 is the number of times it’s moved

121. Tiny original numbers have negative exponents Example #1 Example: Write the following numbers in scientific notation. 12457.656 m 0.000065423 g 128.90 g 0.0000007532 m 1.24567656  10 m 4 6.5423  10 g -5 1.2890  10 m 2 7.532  10 m -7 Large original numbers have positive exponents

122. Reading Scientific Notation A positive power of ten means you need to make the number bigger and a negative power of ten means you need to make the number smaller Move the decimal place to make the number bigger or smaller the number of times of the power of ten

123. Example #2 Example: Write out the following numbers. 1.37  10 4 m 2.875  10 2 g 8.755  10 -5 g 7.005  10 -3 m

124. 1.37  10 4 m 2.875  10 2 g 8.755  10 -5 g 7.005  10 -3 m Example #2 Example: Write out the following numbers. 13700 m 287.5 g 0.00008755 m 0.007005 m Move the decimal “the power of ten” times Positive powers = big numbers. Negative powers = tiny numbers

125. Scientific Notation & Significant Digits Scientific Notation is more than just a short hand. Sometimes there isn’t a way to write a number with the needed number of significant digits …unless you use scientific notation!

126. Take a look at this… Write 120004.25 m with 3 significant digits 120004.25 m 120000. m 120000 m 1.20  10 5 m 120. m 8 significant digits 6 significant digits 2 significant digits 3 significant digits Remember…120 isn’t the same as 120000! Just because those zero’s aren’t significant doesn’t mean they don’t have to be there! This answer isn’t correct!

127. Examples #3 Example: Write the following numbers in scientific notation. 120347.25 g with 3 sig digs 0.0002307 m with 2 sig digs 12056.76 mL with 4 sig digs 0.00000024 g with 2 sig digs

128. Examples #3 Example: Write the following numbers in scientific notation. 120347.25 g with 3 sig digs 0.0002307 m with 2 sig digs 12056.76 mL with 4 sig digs 0.00000024 g with 2 sig digs Move the decimal after the first non-zero number Start counting significant figures from that first non-zero number Round when you get the wanted number of significant digits Remember—large numbers are positive powers of ten & tiny numbers have negative powers of ten! 1.20 × 10 5 g 2.3 × 10 -4 g 1.206 × 10 4 g 2.4 × 10 -7 g

129. Let’s Practice Example: Write the following numbers in scientific notation. 0.0007650 g with 2 sig digs 120009.2 m with 3 sig digs 239087.54 mL with 4 sig digs 0.0000078009 g with 3 sig digs Example: Write out the following numbers 1.34 × 10 -3 g 2.009  10 -4 mL 3.987  10 5 g 2.897  10 3 m

130. Let’s Practice 7.7 × 10 -4 g 1.20 × 10 5 g 2.391 × 10 5 g 7.80 × 10 -6 g Example: Write the following numbers in scientific notation. 0.0007650 g with 2 sig digs 120009.2 m with 3 sig digs 239087.54 mL with 4 sig digs 0.0000078009 g with 3 sig digs Example: Write out the following numbers 1.34 × 10 -3 g 2.009  10 -4 mL 3.987  10 5 g 2.897  10 3 m 0.00134 g 0.0002009 mL 39870 g 2897 m

131. Chapter 1—Scientists’ Tools Summary

132. Chemistry is an Experimental Science You have learned the following:  Common characteristics of scientific processes  How observations & measurements are taken accurately & precisely during those scientific processes  How to design a lab yourself to answer questions  How to convert units you’ve measured in to ones that are more useful to calculate with  How to report answers to calculations with the correct number of significant digits to represent the accuracy of the measurements you took in the lab  How to use scientific notation to express the correct number of significant figures

133. What did you learn about Scientists’ tools?

134. Chemistry is an Experimental Science Common characteristics Although no one method, there are Careful observation s Accurate & precise measurements Design your own labs Unit conversions Significant digit rules Scientific Notation Are used when you include May require When using in calculations, follow May require using