1. Unit 0: Working as a Scientist – Significant Figures AGENDA: DO NOW NOTES WHITE BOARDING LAB GOAL: I can properly record and calculate data with proper significant figures by taking notes, practicing, and performing a lab. Homework: Significant Figures Practice Do Now – What is the difference between the values of 3, 3.0, and 3.00 MondayTuesdayWednesdayThursdayFriday Uncertainty and Measurement Significant Figures ACT Fridays

2. Significant Figures  Instruments are only so precise.  The number of digits reported are considered significant figures.  There are rules for determining the number of significant figures.

3. RULE #1 SIG FIG2 SIG FIGS3 SIG FIGS4 SIG FIGS5 SIG FIG 161718334.2512,375 2 3 4

4. Rules for Significant Figures 1. Non-zero numbers are always significant. Ex. 72.3  has 3 significant figures.

5. RULE #1 SIG FIG2 SIG FIGS3 SIG FIGS4 SIG FIGS5 SIG FIG 161718334.2512,375 2101500103500112,305 3 4

6. Rules for Significant Figures 1. Non-zero numbers are always significant. Ex. 72.3  has 3 significant figures. 2. Zeros between non-zero numbers are always significant. Ex. 60.5  has 3 significant figures.

7. RULE #1 SIG FIG2 SIG FIGS3 SIG FIGS4 SIG FIGS5 SIG FIG 161718334.2512,375 2101500103500112,305 35050.125,00012.0012.000 4

8. Rules for Significant Figures 1. Non-zero numbers are always significant. Ex. 72.3  has 3 significant figures. 2. Zeros between non-zero numbers are always significant. Ex. 60.5  has 3 significant figures. 3.Zeros before (to the left of) non-zero numbers are not significant. Ex. 0.0253  has 3 significant figures

9. RULE #1 SIG FIG2 SIG FIGS3 SIG FIGS4 SIG FIGS5 SIG FIG 161718334.2512,375 2101500103500112,305 35050.125,00012.0012.000 40.0000010.0068502502.0502,340,000

10. 4. All Zeros after (to the right of) non-zero numbers are significant IF there is a decimal point in the number. Ex. 123.00  5 significant figures (decimal) Ex. 12,000  2 significant figures (no decimal) Ex. 120.0  4 significant figures (decimal) Ex. 12,000.  5 significant figures (decimal)

11. Let’s try some together…. How many significant digits are in these numbers? 1.35 g 2.3.57 m 3.3.507 km 4.0.0035 kg 5.2406 L 6..0004 m 7.240.00 g 8.20.04080 g

12. How did you do? 1.35g2 2.3.57m3 3.3.507km4 4.0.0035kg2 5.2406 L4 6..0004m1 7.240.00 g5 8.20.04080 g7

13. White Boards and Sig Figs! Write down your answer on the white board and hold it up when you think that you have the answer!

14. 1.3 x 10 2 2

15. 0.00002 1

16. 4.521 x 10 -4 4

17. 230 2

18. 0.002300 4

19. 302.00 5

20. Rounding Numbers  Often times your calculator will give you more digits than necessary. In these cases you will round. Let try a few. 1. Round 3.515014 to 5 significant figures. = 3.5150 2. Round 3.5150 to 3 significant figures = 3.52 3. Round 3.52 to 1 significant figure = 4 4. Round 3430 to 2 significant figures = 3400

21. Round all of the numbers to four significant figures a. 84791 kg b. 38.5432 g c. 256.75 cm d. 4.9356 m e. 0.00054818 g f. 136,758 kg g. 308,659,000 mm h. 2.0142 ml

22. Round all of the numbers to four significant figures a. 84791 kg = 84790 kg b. 38.5432 g = 38.54 g c. 256.75 cm = 256.8 cm d. 4.9356 m = 4.936 m e. 0.00054818 g = 0.00005482 g or 5.482 x 10 -5 g f. 136,758 kg = 136,800 kg or 1.368 x 10 5 kg g. 308,659,000 mm = 308,700,000mm or 3.087 x 10 8 mm h. 2.0142 ml = 2.014 ml

23. Round the following numbers as asked White Boarding!!!!!!

24. Round 23.21004 to 3 sig figs 23.2

25. Round 102,000 to 1 sig fig 100,000

26. Round 234,523.2 to 3 sig figs 235,000

27. Round 910,230 to 4 sig figs 910,200

28. Round 54.530 to 2 sig figs 55

29. Round 46,000,000 to 1 sig figs 50,000,000

30. Calculations with significant figures 1. For multiplication and division, the answers should be rounded off to the same number of significant figures in the measurement with the fewest significant figures Ex. 3.01 x 2.0 = 6.02  6.0 Ex. 45 / 9.00 = 5.00  5.0

31. Example I ride my bike to school. The distance is 4.1 miles. The other day it took 25.7 minutes. What was my average speed, in miles per minute? 4.1 mi = 0.1595440793 mi 25.7 min min 4.1 mi = 0.16 mi 25.7 min min

32. Working with "Sig Figs" Why did I convert 0.1595440793 mi/min to 0.16 mi/min and not something else? Rules for working with significant figures: Rounding Sig figs in calculations

33. Addition and Subtraction 2.For addition and subtraction, the answers should be rounded off to the same number of decimal points as the measurement with the fewest decimal places. Ex. 2.56 + 2.1 = 4.66  4.7 Ex. 34.232 + 22.4 = 56.632  56.6

34.  Solve 4.00134 - 2.02 + 0.000071 4.00134 - 2.02 + 0.000071 = 1.981411 = 1.98  Solve 180,000 – 24,420 – 31,086 180,000 – 24,420 – 31,086 = 124,494 = 120,000 Precision decreases

35. Perform the following calculations and round according to significant figures or decimal places. White Boarding!!!!!

36. 40.50 + 2.3 42.8

37. 3450 + 2 3450

38. 1,205 + 3,100.4 4,305

39. 10 - 9.9 0

40. 5.5 + 3.7 + 2.97 12.2

41. 4.5 - 5.00 -.5

42. 7.77 / 2.3 3.4

43. 3.890 / 121.0321

44. 120 x 0.0002.02

45. 0.00005 x 538.03

46. Practice: 1)4.5 + 2.34 = _____________________ 2)2) 4.5 – 5 = ________________________ 3) 6.00 + 3.411 = _____________________ 4) 3.4 x 2.32 = _______________________ 5) 7.77 / 2.3 = ______________________ 6) 3.890 / 121 = ______________________

47. 7) 1200 x 23.4 = ______________________ 8) 120 x 0.0002 = _____________________ 9) 78.5 + 0.0021 + 0.0099 = ___________ 10) (3.4 x 8.90) x (2.3 + 9.002) = _________ 11) (2.31 x 10 3 ) / (3.1 x 10 2 ) = ___________ 12) 0.0023 + 65 = __________________

48. Measurement Lab with Significant Figures  Objective: You will make many measurements in this experiment, and the goal is to record each measurement with the correct number of significant figures, proper units, and uncertainties. You will also make some simple calculations so make sure to use proper significant figures in the calculations. - Digital measurement devices (balances and computer probes): Record all digits in the measurement given by the instrument, include the proper units, and record uncertainty (+/- the last shown digit). - Analog measurement devices: Record all known digits, and estimate one digit “between the lines.” Be sure to include units and uncertainty (+/- half of the smallest division on the scale). - First Read through the lab and come up with a detailed data table to record important information on a separate sheet of paper.

49. Length/Area: Measure the length and width of the piece of cardboard. Record the measurement in centimeters, paying close attention to recording the correct number of significant digits and make sure to include uncertainty.  Calculate the area of the paper, using the proper units (cm 2 ) and significant figures. Volume: Use graduated cylinders to measure volume  Obtain approximately 8 mL of water in a small beaker. Add the water to the 10-mL graduated cylinder and measure the volume. Record the volume, paying close attention to the significant figures. Be sure to include the proper units and uncertainty.  REPEAT FOR TWO MORE TRIALS (this means you will find the volume three times total)  Find the average of the three trials be sure to include the proper units and significant figures. Mass: Use a balance to measure mass  Obtain a weighing boat record the mass of the boat OR zero the balance.  Find the mass of each of the objects in the PROCEDURE #3 bag individually paying close attention to the significant figures. Be sure to include the proper units and uncertainty.  Find the total mass of all of the objects together. Make sure to use proper rules for addition in terms of significant figures. Temperature: Use a thermometer or temperature probe  Using a graduated cylinder measure approximately 150mL of distilled water into a 250 mL Erlenmeyer flask.  Heat the water to boiling using the hot plate.  Carefully record the temperature of the boiling water using the thermometer and the correct number of significant figures. Be sure to record the proper units.  Assuming that the accepted value for water’s boiling point is 100.0°C, calculate the percent error.