1. Two important points in measurement
Accuracy & Precision
Two important points in measurement

2. Accuracy and Precision At the conclusion of our time together, you should be able to:
Explain the difference between the accuracy and precision
Give examples of accuracy and precision

3. Accuracy
Accuracy = the extent to which a measured value agrees with a standard value
Accuracy of a device must be checked
Does it read a proper accepted value?
Beware of Parallax – the apparent shift in position when viewed at a different angle.

4. Graduated Cylinder – Meniscus and Parallax

6. Example: Accuracy
Who is more accurate when measuring a book that has a true length of 17.0 cm?
Susan:
17.0 cm, 16.0 cm, 18.0 cm, 15.0 cm
Amy:
15.5 cm, 15.0 cm, 15.2 cm, 15.3 cm

7. Murphy's Laws of Science and Technology
Technology is dominated by those who manage what they do not understand.

8. Precision
Precision = the degree of exactness of a measurement that is repeatedly recorded.
Which set is more precise?
18.2 , 18.4 , 18.35
17.9 , 18.3 , 18.85
16.8 , 17.2 , 19.44

9. Example: Precision
Who is more precise when measuring the same 17.0 cm book?
Susan:
17.0 cm, 16.0 cm, 18.0 cm, 15.0 cm
Amy:
15.5 cm, 15.0 cm, 15.2 cm, 15.3 cm

10. Accuracy vs. Precision High Accuracy High Precision High Precision
Low Accuracy

11. Can you hit the bull's-eye?
Three targets with three arrows each to shoot.
Both accurate and precise
Precise but not accurate
Neither accurate nor precise
How do they compare?
Can you define accuracy vs. precision?

12. Why Is There Uncertainty?
Measurements are performed with instruments, and no instrument can read to an infinite number of decimal places
Which of the instruments below has the greatest uncertainty in measurement?

13. Braille dots are on the keypads of drive-up ATM's?
The Scientific Method begins with Questions about the World Around You. Ever Wonder Why?...
Braille dots are on the keypads of drive-up ATM's? 13

14. Accuracy and Precision Let’s see if you can:
Explain the difference between the accuracy and precision
Give examples of accuracy and precision

15. Exit Quiz: Evaluate whether the following are precise, accurate or both.
High Accuracy
High Precision
Low Accuracy
Low Precision
Low Accuracy
High Precision

16. Significant Figures
In Measurements

17. Significant Figures At the conclusion of our time together, you should be able to:
Explain what significant figures are in a measurement
Determine the number of significant figures in any measurement

18. Significant Figures
The significant figures in a measurement include all of the digits that are known, plus one last digit that is estimated.
The numbers reported in a measurement are limited by the measuring tool.

19. How many sig figs are there in a given measurement?

20. Measurement and Significant Figures
Every experimental measurement has a degree of uncertainty.
The volume, V, at right is certain in the 10’s place, 10mL<V<20mL
The 1’s digit is also certain, 17mL<V<18mL
A best guess is needed for the tenths place.

21. To indicate the precision of a measurement, the value recorded should use all the digits known with certainty, plus one additional estimated digit that usually is considered uncertain by plus or minus 1.
No further insignificant digits should be recorded.
The total number of digits used to express such a measurement is called the number of significant figures.
All but one of the significant figures are known with certainty. The last significant figure is only the best possible estimate.

22. Below are two measurements of the mass of the same object
Below are two measurements of the mass of the same object. The same quantity is being described at two different levels of precision or certainty.

23. 15 Helpful Hints On The Lab Report from Mr. T’s Vast Lab Experience!!!
Hint #5. A record of data is essential. It fools the instructor into thinking that you were working. 23

24. Reading a Meterstick
. l I I I I cm
First digit (known) = ?? cm
Second digit (known) = ? cm
Third digit (estimated) between cm
Length reported = cm
or cm
or cm

25. Known + Estimated Digits
In 2.77 cm…
Known digits 2 and 7 are 100% certain
The third digit 7 is estimated (uncertain)
In the reported length, all three digits (2.77 cm) are significant including the estimated one

26. . l8. . . . I . . . . I9. . . . I . . . . I10. . cm Learning Check
What is the length of the line?
1) cm
2) cm
3) cm
How does your answer compare with your neighbor’s answer? Why or why not?

27. Zero as a Measured Number
. l I I I I cm
What is the length of the line?
First digit ?? cm
Second digit ? cm
Last (estimated) digit is cm

28. Always estimate ONE place past the smallest mark!
11.5 mL

29. So how many sig figs are there in a given measurement?
52.8 mL

30. Be Wary of Wealth and Success!!
Charles Schwab, president of the largest steel company, died a pauper.
Edward Hopson, president of the largest gas company, became insane.
Richard Whitney, president of the New York Stock Exchange, was released from prison to die at home.
Cosabee Rivermore, the Great Bear of Wall Street, died of suicide.

31. Be Wary of Wealth and Success!!
Gene Sarazan, the U.S. Open and the PGA Golf Tournaments Champion, went on to live a full and happy life playing golf and remaining solvent.
Conclusion: Stop worrying about business and start playing more golf!! 31

32. How to Determine Significant Figures in a Problem
Use the following rules:

33. Rule #1 Every nonzero digit is significant Examples: 24 = 2 3.56 = 3
24 = 2
3.56 = 3
= 1

34. Rule #2 – Sandwiched 0’s 3 Zeros between non-zeros are significant
Examples:
7003 = 4 = 3

35. Rule #3 – Leading 0’s
Zeros appearing in front of non-zero digits are not significant
Act as placeholders
Can’t be dropped, show magnitude
Examples:
= 2 = 3

36. Rule #4 – Trailing 0’s with DP
Zeros at the end of a number and to the right of a decimal point are significant.
Examples:
= 4
= 4 = 3

37. Rule #5 – Trailing 0’s without DP
Zeros at the end of a number and to the left of a decimal point aren’t significant
Examples:
= 1
27,300 = 3

38. Easier Way to do Sig Figs!!
Pacific/Atlantic P A
If a decimal point is present, start on the Pacific (P) side and draw an arrow through the number until you hit a non-zero digit. Count all numbers without an arrow through them.
If a decimal is absent, start on the Atlantic (A) side and draw an arrow through the number until you hit a non-zero digit.

39. Examples:
grams
decimal present, start on “P” side, draw arrow, count digits without an arrow through it.
Answer = 6
10,100 centimeters
Decimal absent, start on “A” side, draw an arrow, count digits without an arrow through it.
Answer = 3

40. Learning Check
State the number of significant figures in each of the following:
A m
B L
C g
D m
E. 2,080,000 bees

41. Learning Check A. Which answer(s) contain 3 significant figures?
1) ) ) 4760
B. All the zeros are significant in
1) ) ) x 103
C. 534,675 rounded to 3 significant figures is
1) ) 535, ) 5.35 x 105

42. Learning Check
In which set(s) do both numbers contain the same number of significant figures?
1) m and m
2) m and 40 m
3) m and 150,000 m