1. Precision, Accuracy and Significant Figures Notes

2. Today’s Objectives Compare and contrast accuracy and precision. Identify the purpose of significant figures. Multiply, divide and add and subtract using significant figure rules.

3. Precision vs. Accuracy

7. Accuracy Accuracy is how close something comes to an accepted standard.

8. Precision Precision - how fine the divisions or segments are and how repeatable the results.

9. Accurate = Correct Precision = Consistent

10. Ideally an instrument is both accurate and precise

11. Precision can add to accuracy if the instrument is calibrated correctly.  Deduct if not  Example: Tare (zero) a scale

12. Significant Figures Purpose Significant digits carry the precision of the instrument used. Why do them?  Consistency between people  Ensures that the precision of the results only reflect the precision of the least precise measuring tool

13. If a sprinter is measured to have completed a 100.0 m race in 11.71 seconds, what is his average speed? Average speed = 8.53970965 m/s Can we really measure a sprinter’s speed that precisely?

14. Other Options Include: 8.53970965 m/s 8.5397097 m/s 8.539710 m/s or 8.53971 (What is the difference?) 8.53971 m/s 8.5397 m/s 8.540 m/s or 8.54 m/s (What is the difference?) 8.54 m/s 8.5 m/s 9 m/s Which would you choose?

15. Candle with a mass of 14.143g 2.7 hours is the burn time.  14.143g/2.7 hrs = 5.238148148 g/hr This number magically became more precise

16. One who makes a square’s side 5.1 cm x 5.1 cm is not confident that the square is exactly 26.013496870584764240556 cm 2. Nor would it be useful to say the square is 30 cm 2 One has to be careful claiming a greater precision than what is justified

17. A good rule of thumb  No final answer should have any more precision attached to it than the LOWEST precision found among the numbers being worked. Another words… you answer should not have more digits than the original numbers calculated

18. Significant Figures Practice

19. Sig Fig – Rules Nonzero numbers are always significant 1.234 3876493

20. Sig Fig – Rules All final zeros after the decimal point are significant 1.000000, 345.600

21. Sig Fig – Rules Zeros between two other significant digits are always significant. 1.001, 234.01, 3.404040

22. Sig Fig – Rules Zeros used solely as placeholders are not significant. 0.0002, 0.0231, 0.003040

23. Practice Time

24. How Many Sig Figs? 100 10.98 0.0034 0.0480

25. How Many Sig Figs? 6.0490 303000 4.030.00000010

26. Calculating With Sig Figs Scientific Notation shows you how many sig. figs are in the number. Ex.2.5x10 2 This is 2 sig. figs. 1.0000x10 -23 This has 5 sig. figs.

27. Calculating With Sig Figs Adding and Subtracting Sig. Figs. RULE: When adding or subtracting your answer can only show as many decimal places as the measurement having the fewest number of decimal places.  Example: When we add 3.76 g + 14.83 g + 2.1 g = 20.69 g  20.7g

28. Calculating With Sig Figs Multiplying and Dividing with Sig. Figs. RULE: When multiplying or dividing, your answer may only show as many significant digits as the multiplied or divided measurement showing the least number of significant digits. Example: When multiplying 22.37 cm x 3.10 cm x 85.75 cm = 5946.50525 cm3 We look to the original problem and check the number of significant digits in each of the original measurements: Our answer can only show 3 significant digits because that is the least number of significant digits in the original problem. 5946.50525 shows 9 significant digits, we must round to the tens place in order to show only 3 significant digits. Our final answer becomes 5950 cm3.