1. Section 5.1 Scientific Notation and Units Steven S. Zumdahl Susan A. Zumdahl Donald J. DeCoste Gretchen M. Adams University of Illinois at Urbana-Champaign Chapter 5 Measurements and Calculations

2. Section 5.1 Scientific Notation and Units 1.To use the metric system to measure length, volume and mass Objectives

3. Section 5.1 Scientific Notation and Units Measurement A quantitative observation Consists of 2 parts  Number  Unit – tells the scale being used

4. Section 5.1 Scientific Notation and Units B. Units Units provide a scale on which to represent the results of a measurement.

5. Section 5.1 Scientific Notation and Units B. Units There are 3 commonly used unit systems.  English  Metric (uses prefixes to change the size of the unit)  SI (uses prefixes to change the size of the unit)

6. Section 5.1 Scientific Notation and Units C. Measurements of Length, Volume and Mass Length  Fundamental unit is meter  1 meter = 39.37 inches Comparing English and metric systems

7. Section 5.1 Scientific Notation and Units C. Measurements of Length, Volume and Mass

8. Section 5.1 Scientific Notation and Units C. Measurements of Length, Volume and Mass Volume  Amount of 3-D space occupied by a substance  Fundamental unit is meter 3 (m 3 )

9. Section 5.1 Scientific Notation and Units C. Measurements of Length, Volume and Mass Mass  Quantity of matter in an object  Fundamental unit is kilogram

10. Section 5.1 Scientific Notation and Units LET’S PRACTICE.. Use the worksheet provided by your teacher.

11. Section 5.2 Uncertainty in Measurement and Significant Figures 1.To learn how uncertainty in a measurement arises 2.To learn to indicate a measurement’s uncertainty by using significant figures 3.To learn to determine the number of significant figures in a calculated result Objectives

12. Section 5.2 Uncertainty in Measurement and Significant Figures A. Uncertainty in Measurement A measurement always has some degree of uncertainty.

13. Section 5.2 Uncertainty in Measurement and Significant Figures A. Uncertainty in Measurement Different people estimate differently. Record all certain numbers and one estimated number.

14. Section 5.2 Uncertainty in Measurement and Significant Figures B. Significant Figures Numbers recorded in a measurement.  All the certain numbers plus first estimated number

15. Section 5.2 Uncertainty in Measurement and Significant Figures B. Significant Figures Rules for Counting Significant Figures 1.Nonzero integers always count as significant figures 1457 4 significant figures

16. Section 5.2 Uncertainty in Measurement and Significant Figures B. Significant Figures Rules for Counting Significant Figures 2.Zeros a.Leading zeros – never count 0.25 2 significant figures

17. Section 5.2 Uncertainty in Measurement and Significant Figures B. Significant Figures Rules for Counting Significant Figures 2.Zeros b.Captive zeros – always count 1.08 3 significant figures

18. Section 5.2 Uncertainty in Measurement and Significant Figures B. Significant Figures Rules for Counting Significant Figures 2.Zeros c.Trailing zeros – count only if the number is written with a decimal point 100 1 significant figure 100. 3 significant figures 120.0 4 significant figures

19. Section 5.2 Uncertainty in Measurement and Significant Figures B. Significant Figures Rules for Counting Significant Figures 3.Exact numbers – unlimited significant figures Not obtained by measurement Determined by counting 3 apples Determined by definition 1 in. = 2.54 cm, exactly

20. Section 5.2 Uncertainty in Measurement and Significant Figures B. Significant Figures

21. Section 5.2 Uncertainty in Measurement and Significant Figures B. Significant Figures Rules for Multiplication and Division The number of significant figures in the result is the same as in the measurement with the smallest number of significant figures.

22. Section 5.2 Uncertainty in Measurement and Significant Figures B. Significant Figures Rules for Addition and Subtraction The number of significant figures in the result is the same as in the measurement with the smallest number of decimal places.

23. Section 5.2 Uncertainty in Measurement and Significant Figures Concept Check You have water in each graduated cylinder shown. You then add both samples to a beaker (assume that all of the liquid is transferred). How would you write the number describing the total volume? 3.1 mL What limits the precision of the total volume?

24. Section 5.2 Uncertainty in Measurement and Significant Figures LET’S PRACTICE Use the worksheet provided by your teacher

25. Section 5.3 Problem Solving and Unit Conversions 1.To learn how dimensional analysis can be used to solve problems Objectives

26. Section 5.3 Problem Solving and Unit Conversions A. Tools for Problem Solving Be systematic Ask yourself these questions  Where do we want to go?  What do we know?  How do we get there?  Does it make sense?

27. Section 5.3 Problem Solving and Unit Conversions A. Tools for Problem Solving Conversion factors are built from an equivalence statement which shows the relationship between the units in different systems. Converting Units of Measurement

28. Section 5.3 Problem Solving and Unit Conversions A. Tools for Problem Solving 2.85 cm = ? in. Converting Units of Measure Does this answer make sense? 2.85 cm  conversion factor = ? in. Possible conversion factors Equivalence statement2.54 cm = 1 in.

29. Section 5.3 Problem Solving and Unit Conversions A. Tools for Problem Solving Tools for Converting from One Unit to Another Step 1 Find an equivalence statement that relates the 2 units. Step 4 Make sure you have the correct number of significant figures. Step 3 Multiply the original quantity by the conversion factor. Step 2 Choose the conversion factor by looking at the direction of the required change (cancel the unwanted units).

30. Section 5.3 Problem Solving and Unit Conversions Example #1 A golfer putted a golf ball 6.8 ft across a green. How many inches does this represent? To convert from one unit to another, use the equivalence statement that relates the two units. 1 ft = 12 in The two conversion factors are:

31. Section 5.3 Problem Solving and Unit Conversions Derive the appropriate conversion factor by looking at the direction of the required change (to cancel the unwanted units). Example #1 A golfer putted a golf ball 6.8 ft across a green. How many inches does this represent?

32. Section 5.3 Problem Solving and Unit Conversions Multiply the quantity to be converted by the conversion factor to give the quantity with the desired units. Example #1 A golfer putted a golf ball 6.8 ft across a green. How many inches does this represent?

33. Section 5.3 Problem Solving and Unit Conversions Example #2 An iron sample has a mass of 4.50 lbs. What is the mass of this sample in grams? (1 kg = 2.2046 lbs; 1 kg = 1000 g)

34. Section 5.3 Problem Solving and Unit Conversions Concept Check What data would you need to estimate the money you would spend on gasoline to drive your car from New York to Los Angeles? Provide estimates of values and a sample calculation.

35. Section 5.3 Problem Solving and Unit Conversions B. Temperature Conversions There are three commonly used temperature scales, Fahrenheit, Celsius and Kelvin.

36. Section 5.3 Problem Solving and Unit Conversions B. Temperature Conversions Note that  The temperature unit is the same size.  The zero points are different. To convert from Celsius to Kelvin, we need to adjust for the difference in zero points. Converting between the Kelvin and Celsius Scales

37. Section 5.3 Problem Solving and Unit Conversions B. Temperature Conversions Converting between the Kelvin and Celsius Scales

38. Section 5.3 Problem Solving and Unit Conversions B. Temperature Conversions Note Converting between the Fahrenheit and Celsius Scales  The different size units  The zero points are different To convert between Fahrenheit and Celsius, we need to make 2 adjustments. or

39. Section 5.3 Problem Solving and Unit Conversions C. Density Density is the amount of matter present in a given volume of substance. Common units are g/cm 3 or g/mL.

40. Section 5.3 Problem Solving and Unit Conversions C. Density

41. Section 5.3 Problem Solving and Unit Conversions Example #1 A certain mineral has a mass of 17.8 g and a volume of 2.35 cm 3. What is the density of this mineral?

42. Section 5.3 Problem Solving and Unit Conversions Example #2 What is the mass of a 49.6-mL sample of a liquid, which has a density of 0.85 g/mL?