1. PREREQUISITES!!! Lecture Homework: Reading - Chapter 2, sections 5-8
Problems from chapter 2, DUE MONDAY
#’s 5, 7, 8, 11, 13, 33, 35, 37, 38, 39, 40, 43, 45, (all)
Lab Homework – Experiment #1
Read intro and lab CAREFULLY
PREREQUISITES!!!

2. Uncertainty All about uncertainty
ALL measurements have some uncertainty
between 11.5 and 12 cm
about cm
about 11.7 or 11.8 cm

3. Uncertainty
Time’s up!!
5:02
5:01
5:00

4. Uncertainty All about uncertainty
ALL measurements have some uncertainty
about 11.8 cm

5. Uncertainty All about uncertainty
ALL measurements have some uncertainty

6. Uncertainty Exact numbers: Examples:
1 foot =
1 kilometer =
1 mile =
24 hours =
Have NO uncertainty because these numbers are DEFINED
Will never affect “significant figures”

7. Uncertainty Counted numbers: Examples Also have no uncertainty
I have 11 fingers
there are 11 dogs
Also have no uncertainty
Will never affect “significant figures”

8. Uncertainty Measured number ALWAYS have some uncertainty to them
Examples
I live 6 and a half miles away
I drink 1.5 liters of water a day
This bench is…
ALWAYS have some uncertainty to them
Will always affect “significant figures”

9. Uncertainty and Measurements
State the digits you can be sure of!
Guess the next digit! (and only the next digit)
I KNOW it is between 11 cm and 12 cm
measurement:
11.8 cm
graduations (marks): 1 cm
uncertainty: ± 0.1 cm

10. Uncertainty and Measurements
State the digits you can be sure of!
Guess the next digit! (and only the next digit)
I KNOW it is between 11.8 cm and 11.9 cm
measurement:
11.84 cm
graduations (marks): 0.1 cm
uncertainty: ± 0.01 cm

11. Uncertainty and Measurements
State the digits you can be sure of!
Guess the next digit! (and only the next digit)
between 500 cm and 600 cm
measurement:
520 cm
graduations (marks): 100 cm
uncertainty: ± 10 cm

12. Uncertainty and Measurements
If your instrument has an uncertainty of ± 0.01 mL, your measurement will end with or .09
If your instrument has an uncertainty of ± 0.2 g, your measurement will end with , or .8
If your instrument has an uncertainty of ± cm, your measurement will end with or .005

13. Uncertainty and Measurements
Which of the following would be correct if measured on the ruler below?
assume ± 0.1 cm uncertainty
a) 1.0 cm b) 1.50 cm c) 1.55 cm
d) 1.6 cm e) 2.00 cm

14. Uncertainty and Measurements
Which of the following would be correct if measured on the ruler below? (This ruler has an uncertainty of ± 0.05 cm)
a) 0.5 cm b) 0.50 cm c) cm
d) 0.75 cm e) cm

15. 11.84 cm Significant Figures 4 significant figures
Significant figures tell you about the uncertainty in a measurement.
Significant figures include all CERTAIN (known) digits, and ONE UNCERTAIN (guessed) digit
11.84 cm
4 significant figures

16. 520 cm Significant Figures 2 significant figures
Significant figures include all CERTAIN (known) digits, and ONE UNCERTAIN (guessed) digit
520 cm
2 significant figures

17. How many Sig. Figs.? Two rules:
#1) If there IS a decimal point in the number:
Start at right of number and count until the LAST non-zero digit

18. 2 3 . 2 8 1 . 6 8 1 . How many Sig. Figs.? 9 significant figures2 8 1
9 significant figures . 6 8
4 significant figures 1 .
6 significant figures

19. How many Sig. Figs.? Two rules:
#1) If there IS a decimal point in the number:
Start at right of number and count until the LAST non-zero digit
#2) If there is NOT a decimal point in the number
Start at left of number and count until the LAST non-zero digit

20. 7 4 2 9 3 2 3 8 1 How many Sig. Figs.? 5 significant figures8
4 significant figures 1
1 significant figure

21. Significant Practice
0.0005
320000
8900.
0.1528
6 s.f.
7 s.f.
1 s.f.
5 s.f.
2 s.f.
4 s.f.

22. Rounding Numbers Find the last significant digit.
If the next digit to the right is 4 or less, leave the last significant digit alone.
If the next digit to the right is 5 or more, round the last significant digit up.
Put large numbers into scientific notation BEFORE rounding

23. (3 s.f.)
(3 s.f.) =
(5 s.f.)
(5 s.f.) =
(2 s.f.)
(2 s.f.) =
(3 s.f.)
(3 s.f.)
= 0.66
= 0.660
(5 s.f.)
(5 s.f.) =
(5 s.f.)
(5 s.f.) =

24. Sig. Figs. in Calculations
Two rules:
#1) Multiplication and Division
The value in the calculation that has the FEWEST number of sig. figs. determines the number of sig. figs. in your answer.

25. Calculations with Sig. Figs.
Multiplication and division
The value in the calculation that has the FEWEST number of sig. figs. determines the number of sig. figs. in your answer.
1.5 x
= 1
.9881
= 11
2 s.f.
5 s.f.
6.127 x = 6 09 =
4 s.f.
6 s.f.

26. Calculations with Sig. Figs.
/ 456.0
= 2.03 3
730263
= 2.034
6 s.f.
4 s.f.
/ 2
= 0.000 7 95 =
3 s.f.
1 s.f.
6 s.f.
3 s.f.
= 18 8 =
4 s.f.

27. Some Practice
x 112.3
78132/2.50
x x
500 x
99950
31300
0.0050
0.1

28. Sig. Figs. in Calculations
Two rules:
#1) Multiplication and Division:
The value in the calculation that has the FEWEST number of sig. figs. determines the number of sig. figs. in your answer.
#2) Addition and Subtraction:
The value in the calculation that has the FEWEST decimal spots determines the number of decimal spots in your answer.

29. Adding and subtracting with sig. figs.
7 decimal places
6 decimal places _ _ =
answer can only
be precise to the
6th decimal place

30. Adding and subtracting with sig. figs.
4 decimal places
7 decimal places =
answer can only
have 4 decimal places

31. Some More Practice 23.67 – 75 5502.8 + 24 + 0.01 0.109 + 0.09 – 0.955
-51
5527
-0.76
100.

32. Sig. Figs. in Calculations
Two rules:
#1) Multiplication and Division:
The value in the calculation that has the FEWEST number of sig. figs. determines the number of sig. figs. in your answer.
#2) Addition and Subtraction:
The value in the calculation that has the FEWEST decimal spots determines the number of decimal spots in your answer.

33. Mixed Operations with sig. figs.
1) Do inside parenthesis first
2) Mark the last significant digit you are going to keep in that step
3) Finish calculations
4) Report answer to correct number of sig. figs.
4 sig. figs.  
5 sig. figs.