2. Math vs. Science mathematicianTo a mathematician: 73 = 73.0 = 73.00 = 73.000 etc. scientistTo a scientist, these numbers mean very different things.

3. Numbers in Science 1.Counts 1.Counts are exact and have an infinite number of significant figures. There are 31 desks in room 267 means 31.000  desks.

4. Numbers in Science 2.Definitions 2.Definitions are exact and have an infinite number of significant figures. 1 meter = 100 cm really means 1.000  m = 100.000  cm. 12 inches = 1 foot really means 12.000  inches = 1.0000 … foot

5. Numbers in Science 3.Measurements 3.Measurements are never perfect and they have a finite number of significant figures. The number of sig figs in a measurement depends on the calibration of the measuring device.

6. What is Calibration? The calibration of a measuring device is the spacing between the two closest lines.

7. Reporting Data: The RULE Report one decimal place beyond the calibration of your measuring device. In other words: Report all the numbers you know for sure plus one that you estimate.

8. source What’s the reading? Calibration = 1 ml Calibration is to the one’s place so you report to the tenth’s place. 67.5 ml You know the 60 and the 7 for sure. You estimate the 0.5.

9. source Calibration is to the tenth’s place. What’s the reading?373.35 g You report to the hundredth’s place.

10. Glassware Cylinder Movie Buret Movie Volume 6, CCA

11. Interpreting Data (What it all means.)

12. DataCalibration 0.9655 m Know the tenth, the hundredth, and the thousandth for sure. Estimated the ten- thousandth. Device was calibrated to the __________ of a meter. 1.785 g Know the 1, the tenth, and the hundredth for sure. Estimated the thousandth. Device was calibrated to _________ of a gram. 13.2 ml Know the 10 and the 3 for sure. Estimated the tenths. Device was calibrated to the _________ place. thousandths hundredth ones

13. Counting Sig Figs (Have to do this when you do calculations with data.)

14. Rules for counting sig figs 1.All non-zero digits are significant. 2.All captive zeros are significant. (Captive is a zero between 2 other sig figs.) never 3.Leading zeros are never significant. 4.Trailing zeros Decimal point  significant No not No decimal point  not significant

15. Once in a blue moon: 5300 cm The middle zero is significant. The ruler was calibrated to the hundreds place. You estimated the 10’s place and it happened to land on a zero. _

16. The Atlantic and Pacific Rule Look to see if the number has a decimal point. (A cheat for counting sig figs.) Decimal point Absent = Atlantic Ocean Decimal point Present = Pacific Ocean

17. source X   X X

18. Decimal point present: non- zeroStart counting at the first non- zero digit and count until the end of the number. 2545.300 g has ? sig figs 0.004530 km has ? sig figs Start on the Pacific (left) side of the number. 7 4

19. Decimal point absent: Start on the Atlantic (right) side of the number. non- zeroStart counting at the first non- zero digit and count until the end of the number. 5400 m has ? sig figs 5431 m has ? sig figs 2 4

20. Calculations with Measurements Multiplication and Division significant figures least number The answer can have only as many significant figures as the measurement with the least number of sig figs.

21. 24.56 cm X 14 cm = a) a) 343.84 cm 2 b) b) 343.8 cm 2 c) c) 343 cm 2 d) d) 340 cm 2

22. Calculations with Measurements Addition and Subtraction decimal places least number The answer can have only as many decimal places as the measurement with the least number of decimal places.

23. 422.63 cm 29.472 cm 115.9 cm ________________ + a) 568.002 cm b) 568.00 cm c) 568.0 cm d) 568 cm