1. BELLWORK 9/13/16 1 Tm = 1012 m 1mm = 10-3 m 1Mm = 106 m
1). Convert 2.5 m to Tm.
2) Convert 7.2 mm to Mm
3) Convert 6.1 mm to Tm

2. Why do we have to learn about Sig Figs?

3. Sig Figs tell you what place to round your answers to.
Your final measurement (answer) can never be more precise than your starting measurement.
To understand that idea, we will discuss accuracy vs. precision

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

5. THE BIG CONCEPT
Accuracy –indicates the closeness of the measurements to the true or accepted value.
Beware of Parallax – the apparent shift in position when viewed at a different angle.
2. Precision - The closeness of the results to others obtained in exactly the same way.

6. Accuracy vs. Precision High Accuracy High Precision High Precision
Low Accuracy

7. Master Archers

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

9. 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

10. Example - Precision Which set is more precise?
A cm , 18.4cm , 18.3cm
B cm , 18.3cm , 18.8cm
C cm , 17.2cm , 19.4cm

11. Recording Measurements
Every experimental measurement has a degree of uncertainty.
The volume, at the right is certain in the 10’s place, Greater than 10ml and less than 20ml
The 1’s digit is also certain, greater than 17ml and less than 20ml.
A best guess is needed for the tenths place.

12. 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

13. Always estimate ONE place past the smallest mark!
11.50mL

14. . 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?

15. 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

16. Precision and Instruments
Do all measuring devices have the same amount of precision?

17. You indicate the precision of the equipment by recording its Uncertainty
Ex: The scale on the left has an uncertainty of (+/- .1g)
Ex: The scale on the right has an uncertainty of (+/- .01g)

19. 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.

20. Checkpoint
Complete the Accuracy and Precision Worksheet with a partner.

21. BELLWORK 9/14/16
CAN YOU DETERMINE THE PRECISION OF DATA USING ONLY THE PERCENTAGE ERROR?
Review answers to accuracy vs. precision worksheet

22. Significant Figures
In Measurements

23. 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.

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

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

26. Rule #2 – Sandwiched 0’s 3 Zeros between non-zeros are significant
Examples:
7003m = 4
40.9m = 3

27. Rule #3 – Leading 0’s
Zeros appearing in front of non-zero digits are not significant
Act as placeholders
Examples:
0. 24m = 2
0.453m = 3

28. Rule #4 – Trailing 0’s with Decimal Points
Zeros to the right of a decimal and after a whole number are significant.
Examples:
43.00g = 4
1.010g = 4
1.50g = 3
g = 2
0.0002g = 1

29. Performing Calculations with Significant Figures
Rule: When adding or subtracting measured numbers, your answer cannot be more precise than the least precise measurement.
Only count the Sig Figs that come after the decimal.

30. Adding and Subtracting
2.45 cm cm = 3.65 cm,
Round off to  3.7 cm
7.432 cm + 2 cm = cm
Round to  9.4cm

31. Multiplication and Division
Rule: When multiplying or dividing, the result can have no more significant figures than the least reliable measurement.
Count all of the Sig figs in the entire number.

32. Examples 75.8 cm x 9.6 cm = ? 56.78 cm x 2.45cm = 139.111 cm2
Round to  139cm2
75.8 cm x 9.6 cm = ?

33. 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

34. 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

35. 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