Measurement

1. Measurement • Metric System • Prefixes • Conversions • Scientific Notation • Writing • Calculating • Significant Figures • Definition • Counting • Calculating • Dimensional Analysis

2. Metric System • AKA: International System (SI) • 1960: international agreement set up to use this system of units • Our “English system” is used within our boundaries, but we use the metric system in international trade. • 1999: NASA $125 million dollar mistake

3. Metric System • Graphic organizer for prefixes • Mnemonic device: The good man King Henry died by drinking chocolate milk Monday night, poor fellow. • Prefixes • Powers of Ten • Place holders • Conversions • Temperature • Kelvin & Celsius Oops!

4. As you come in, The Materials: • Put any email slips on the front desk. • Tarvin Consulting Group supplies • Pen/pencil and paper for a few notes The Plan: • Any questions about Element Quiz scheduled for Friday? • Work on Tarvin Consulting Group activity. (30 min) • Review the metric system. Solve and check 1-4 Practice Problems. • Begin Introductory Metric System Lab. • Discuss scientific notation. (POSSIBLE) The Practice: In your practice packet: Any metric system practice & review examples The Assessment: METRIC SYSTEM QUIZ TOMORROW! Element Quiz on Friday! Old School

5. Sample Element Quiz Questions • Co _______________________ • Cr ________________________ • Sn _______________________ • Copper ____________________ • Sodium ____________________ • Iron ________________________

6. Moving the Decimal T // G // M // k h D base d c m // µ // n // p // f

7. 1-4 PP#1 Convert 83 cm into meters. iRespond Question Fill-In F T // G // M // k h D base d c m // µ // n // p // f A.) 0.83;.83; B.) 0.83 meters C.) D.) E.)

8. 1-4 PP #2 Convert 459 L into milliliters. iRespond Question Fill-In F T // G // M // k h D base d c m // µ // n // p // f A.) 459000;; B.) 459,000 mL C.) D.) E.)

9. 1-4 PP #3 Express 1123 pg in nanograms. iRespond Question Fill-In F T // G // M // k h D base d c m // µ // n // p // f A.) 1.123;; B.) 1.123 ng C.) D.) E.)

10. 1-4 PP #4 Express 0.032 m3 in liters. iRespond Question Fill-In F TRICKY! 1 cm3 = 1 mL Steps: Convert 0.032 m3 to cm3. This equals mL. Convert mL to L. TRY IT. A.) 32;; B.) C.) D.) E.)

11. HOW TO CONVERT 0.032m3 to L • Convert 0.032 m3 to cm3. • Cubed conversions are different from simple meter to centimeter conversions. • Move the decimal 2 spaces to the right to go from meter to centimeter, correct? NOT SO FAST! • Move the decimal 2 spaces for EACH dimension. Since the unit is cubed, we’ll move the decimal 2 spaces to the right X 3! • 0.032 m3 = 32,000 cm3 • Convert mL to L. • Since cm3 = mL, 32,000cm3 = 32,000 mL. • Move the decimal 3 spaces to the left to go from milli to liters. • 32,000 mL = 32 L

12. 1-4 PP #5 Express 2.5 mm in micrometers. iRespond Question Fill-In F T // G // M // k h D base d c m // µ // n // p // f A.) 2500;; B.) 2,500 micrometers C.) D.) E.)

13. 1-4 PP #6 Which is the longer amount of time: 1351 ps or 1.2 ns? iRespond Question Multiple Choice F A.) 1351 ps B.) 1.2 ns T // G // M // k h D base d c m // µ // n // p // f C.) D.) 1351 ps E.)

14. 1-4 PP #7 Which is the larger pressure: 232.1 kPa or 125,487 Pa? iRespond Question Multiple Choice F A.) 232.1 kPa B.) 125,487 Pa C.) T // G // M // k h D base d c m // µ // n // p // f D.) 232.1 kPa E.)

15. 1-4 PP #8 Which is the smaller mass: 285.0 cg or 23.78 dg? iRespond Question Multiple Choice F A.) 285.0 cg B.) 23.78 dg C.) T // G // M // k h D base d c m // µ // n // p // f D.) 23.78 dg E.)

16. 1-4 PP #9 Which is shorter: 175.6 mm or 38.4 cm? iRespond Question Multiple Choice F A.) 175.6 mm B.) 38.4 cm C.) T // G // M // k h D base d c m // µ // n // p // f D.) 175.6 mm E.)

17. 1-4 PP #10a 0.7824 mg to grams iRespond Question Fill-In F T // G // M // k h D base d c m // µ // n // p // f A.) 0.0007824;.0007824; B.) 0.000 782 4 grams C.) D.) E.)

18. 1-4 PP #10b 345,000 ng to grams iRespond Question Fill-In F T // G // M // k h D base d c m // µ // n // p // f A.) 0.000345;.000345; B.) 0.000 345 000 grams C.) D.) E.)

19. 1-4 PP #10c 0.00378 kg to grams iRespond Question Fill-In F T // G // M // k h D base d c m // µ // n // p // f A.) 3.78;; B.) 3.78 grams C.) D.) E.)

20. 1-4 PP #10d 34,981 micrograms to grams iRespond Question Fill-In F T // G // M // k h D base d c m // µ // n // p // f A.) 0.034981;.034981; B.) 0.034 981 grams C.) D.) E.)

21. Scientific Notation • Lazy way to report really BIG or small numbers • Uses powers of ten rather than long strings of zeros • + powers mean BIG numbers • - powers mean small numbers

22. Scientific Notation Expand or contract. • 250 = ______________ • 13,210,000 = ________ • 0.00150 = ___________ • 14 = ________________ • 0.00005 = ____________ • 1.6x10-4 = ____________ • 2.15x105 = ____________ • 1.0x101 = _____________ • 4.3x10-2 = ____________

23. Scientific Notation Check your answers. • 250 = 2.5 x 102 • 13,210,000 = 1.321 x 107 • 0.00150 = 1.5 x 10-3 • 14 = 1.4 x 101 • 0.00005 = 5 x 10-5 • 1.6x10-4 = 0.00016 • 2.15x105 = 215,000 • 1.0x101 = 10 • 4.3x10-2 = 0.043

24. Scientific Notation • Use the EE or EXP button to enter scientific notation. • NEVER use the ^ or x10. • Example: • Enter 6.02 x 1023 into your calculator. • Punch 6.02 as normal. • Then push the EE or EXP button. It replaces the x10. • Lastly, enter 23. • Summary: 6.02EXP23

25. Scientific Notation • 6.02x1023 x 18.998 = ____________ • 5.6x10-8 / 3.2x10-3 = _____________ • 2.5x101 + 3.5x102 = _____________ • 8.45x10-3 x 2.1x101 = ____________ 1. 1.144x1025 2. 1.75x10-5 3. 375 4. 0.17745

26. Density • Density is used to identify substances found in nature. • Density = mass/volume • Common units: g/mL or g/cm3 • mL measures the volume of a liquid. It is NOT a cubed unit. • cm3 measures the volume of a solid where length, width, and height were multiplied together.

27. Density Example of Density: A rectangular sample is found. What is the density? 1. Measure the mass with a balance. 2. Measure the volume with a ruler since it has a normal (regular) shape. 3. Calculate.

28. Density Another Example of Density: A strangely shaped sample is found. What is the density? 1. Measure the mass with a balance. 2. Measure the volume with a graduated cylinder using the water displacement method. 3. Calculate.

29. Density A truth about the density of water: • A 1 cm3box will hold EXACTLY 1 mL of water, and the 1 mL of water will weigh EXACTLY 1 gram! • Therefore, 1 cm3 = 1 mL = 1 gram. • You are going to have a chance to prove this in your lab today using a small blue solid (not hollow) cube.

30. Density Density of a Metal Cube Lab Goals: Test the 1 mL = 1 cm3 rule and determine the type of metal that makes up your group’s cube using density. Steps: Follow the lab steps carefully, and be sure to record any measurements on your paper. You’ll have a very small lab report due on Monday. The specifics of the report are described on your lab handout. If you get stuck, send a group rep to Mrs. Tarvin. NOTE: The copy of the lab at your station should not leave the station. A copy of the lab is on the blog for your use at home.

31. iRespond Question Multiple Choice F A student determines that a piece of an unknown material has a mass of 5.854 g and a volume of 7.57 cm3. What is the density of the material? (Density Practice Problems #1) A.) 0.773 g/cm3 B.) 1.29 g/cm3 C.) 44.4 g/cm3 D.) none of these E.)

32. A student determines that a piece of an unknown material has a mass of 5.854 g and a volume of 7.57 cm3. What is the density of the material? (Density Practice Problems #1) Steps: Density = mass / volume Mass = 5.854 grams; Volume = 7.57 cm3 Notice that the units will be grams/cm3. The problem doesn’t specify certain units, so I can use these. 5.854 gram/7.57 cm3 = 0.773 g/cm3

33. iRespond Question Multiple Choice F Iron has a known density of 7.87 g/cm3. What would be the mass of a 2.5 dm3 piece of iron? Density Practice Problem #2 A.) 1.9675 grams B.) 19.675 grams C.) 196.75 grams D.) 19, 675 grams E.)

34. Iron has a known density of 7.87 g/cm3. What would be the mass of a 2.5 dm3 piece of iron? Density Practice Problem #2 Steps: Density = mass / volume Density = 7.87 g/cm3; Since the units are given for density, I am stuck with them. I cannot plug in a mass unless it is in grams. I cannot plug in a volume unless it is in cm3. Convert 2.5 dm3 to cm3. Move the decimal to the right THREE spaces. 7.87g/cm3 = mass / 2500 cm3 ; mass = 19,675 grams

35. iRespond Question Multiple Choice F Mercury has a density of 13.5 g/cm3. How much space (in mm3) would 50.0 g of mercury occupy? Density Practice Problem #3 A.) 3.70 mm3 B.) 37.0 mm3 C.) 370.0 mm3 D.) 3,700 mm3 E.)

36. Mercury has a density of 13.5 g/cm3. How much space (in mm3) would 50.0 g of mercury occupy? Density Practice Problem #3 Steps: Density = mass / volume Density = 13.5 g/cm3; The mass MUST be in grams, and the volume MUST be in cm3. 13.5 g/cm3 = 50.0 g / volume; REMEMBER – The volume will be in cm3 because of the density units. ALGEBRA HELPFUL HINT: Put a 1 under the density & cross multiply. 13.5 g/cm3 = 50.0 grams 1 volume (13.5 g/cm3)(volume) = (50.0 grams)(1) (13.5 g/cm3) (13.5 g/cm3) volume = 3.70 cm3 = 3,700 mm3

37. iRespond Question Multiple Choice F A sample has a mass of 1.02g and a volume of 1.35cm3, what is the density of the nickel? Density Practice Problems #4 A.) 0.756 g/cm3 B.) 1.38 g/cm3 C.) 1.32 g/cm3 D.) 7.56 g/cm3 E.)

38. What is the density of a material if its mass 2.02g and its volume is 0.500cm3? Density Practice Problem #5 iRespond Question Multiple Choice F A.) 1.01 g/cm3 B.) 4.04 g/cm3 C.) 0.248 g/cm3 D.) 4.48 g/cm3 E.)

39. iRespond Question Multiple Choice F Pure gold has a density of 19.32 g/cm3. How large (in dm3) would a piece of gold be if it had a mass of 318.97 g? Density Practice Problems #6 A.) 16.51 dm3 B.) 1.651 dm3 C.) 0.1651 dm3 D.) 0.01651 dm3 E.)

40. iRespond Question Multiple Choice F How many cm3 would a 55.932 g sample of copper occupy if it has a density of 8.92 g/cm3? Density Practice Problems #7 A.) 0.159 cm3 B.) 499 cm3 C.) 6.27 cm3 D.) 48.9 cm3 E.)

41. Significant Figures hey mrstarvin,   im sitting in my awesome chem lecture hall and we're doing review. i was wondering if you could remind me of what your sigfig tricks were to remember when to count them and when not to.  thanks! alexandra ps, i hope you've got some great classes! I got this email yesterday during 4thpd from UGA

42. Significant Figures Digits in measurement communicate valuable quantitative information. If you know your stuff, the digits can tell you qualitative information, too. Example: Compare the information in these two numbers. Don’t forget to read between the lines! a. 148,300 meters b. 148,336.420 meters

43. Significant Figures Making Measurements Examine the markings on the instrument. Note the smallest mark shown and the unit that you’ll be using. What decimal place does the smallest mark represent? Measure the object as usual, and record all of the obvious markings. THEN, ADD ONE ADDITIONAL DECIMAL PLACE TO YOUR MEASUREMENT. (ONE PAST THE MARKINGS OF THE INSTRUMENT.)

44. Significant Figures Making Measurements The ruler is marked to the nearest 1/10 of a centimeter. In other words, the smallest marking is 0.1 cm. The object measures EXACTLY 5.7 cm according to the obvious markings. In science, we record the one estimated digit beyond the obvious markings. We should record the measurement as 5.70 cm. (Note: Answer has ONE extra decimal place beyond the smallest marking.)

45. Significant Figures Making Measurements What if you disagree with my estimate? What if you believe that the object is not EXACTLY on the 5.7 mark? Then, you would use a different estimated digit. Examples: 5.72 cm or 5.75 cm or 5.79 cm

46. Significant Figures • Analyzing measurement data: • Describing the instrument • Evaluating the “worth” Example: Consider the data recorded below. Length: 3.50 cm Width: 2.150 cm Could these have been made by the same instrument? How sensitive is the instrument?

47. Significant Figures Some instruments are better than others, and we may all estimate different final digits in our measurements. Error is an important consideration in our measurements and calculations then. CONSIDER: What if you were asked to calculate the volume of a block? Volume includes THREE measurements (L x W x H). You could have THREE small errors factoring into your volume answer. Special rules exist in scientific calculations to prevent error from “snowballing” in our answers.

48. Significant Figures Remember, measurements involve estimations, and that can be dangerous when working with volatile chemicals. • Reducing the estimation risk: • When adding or subtracting: • Line up the decimals as usual. • Draw a vertical line at the end of the shortest #. • Add or subtract. Round the answer at the line.

49. Significant Figures Addition and Subtraction Example 35.6 + 4.1 + 4.79 + 2 = Step 2: Draw a vertical line at the end of the shortest #. 35.6 4.1 4.79 + 2 Step 1: Line up the decimals. 35.6 4.1 4.79 + 2 Step 3: Add & round at the line. 46.49 = 46

50. Significant Figures 61.2 meters + 9.35 meters + 8.6 meters 9.44 meters - 2.11 meters 34.61 meters -17.3 meters 8.3 meters x 2.22 meters 8432 meters /12.5 79.2 meters 2. 7.33 meters 3. 17.3 meters 4. 18 meters 5. 675 meters