1. Matter, Measurement, and Problem Solving Reliability of Measurement

2. Reliability of a Measurement Scientific measurement is reported so that every digit is certain except the last one, which is estimated

3. Sources of Error All measurements contain error Determinant error ◦ Consistent error- i.e. issues with calibration Indeterminate error ◦ Cause measurements to fluctuate around true value ◦ Factors beyond control  Air currents, static, etc. ◦ Cannot completely eliminate

4. Significant Figures in Measurements

6. Rules for Significant Figures Exact numbers and definitions have infinite significant figures

7. Practice Identifying Significant Figures 102.400 meters 1,200,000 g 4.3020 x 10 -8 m 2.030 x 10 5 nm 25 students 0.00090 cm 19 cm 3 2.05 x 10 7 g 13 eggs 2.37 x 10 -2 m 300,000,000 m/s 100 cm = 1 m

8. Significant Figures in Calculations Two rules- ◦ addition and subtraction  Place value of significant figures ◦ Multiply and divide  Quantity of significant figures

9. Addition and Subtraction Rules Result carries same number of decimal places as the quantity with fewest decimal places

10. Addition Subtraction Practice 2.5 cm + 0.50 cm + 0.055 cm =

11. Addition Subtraction Practice 416 g - 210 g =

12. Addition Subtraction Practice 160 + 88.50

13. Multiplying and Dividing Rule Result contains same number of significant figures as factor with fewest significant figures

14. Multiplying and Dividing Practice 0.020 cm x 50 cm x 11.1 cm =

15. Multiplying and Dividing Practice 0.530 g / 0.1010 mL =

16. Multiplying and Dividing Practice 2.31 cm x 1.5 cm=

17. Multiplying and Dividing Practice 1300 x 5.9980 =

18. Precision vs. Accuracy Accuracy- how close the measured value is to actual value- how exact it is Precision- how close results are to one another

19. Accuracy vs. Precision

20. Percent Error Can apply to single measurement Expresses how much measurement deviates from true or accepted value

21. Percent Error Practice At a track meet, you time a friend running 100 m in 11.00 seconds. The officials time her at 10.67 seconds. What is your percentage error?

22. Error of Multiple Measurements Precision or reproducibility- calculate average

23. Standard Deviation How much are the measurements off by?

24. Example of Standard Deviation