1. Measurement I. Units of Measurement (p.34-45) Number vs. Quantity
SI Base Units & Prefixes
Derived Units
Density Calculations

2. Number vs. Quantity
Quantity - number + unit
UNITS MATTER!!

3. Measurement is central to Physics
Metric system: the set of units used for scientific measurements.
SI Units: there are seven base SI units and all other units are derived from these.

4. SI Units Quantity Base Unit Symbol Length meter m Mass kilogram kg
Time
second s
Temp
kelvin K
Current
ampere A

5. SI Units Prefix Symbol Factor mega- M 106 kilo- k 103 deci- d 10-1
centi- c
10-2
milli- m
10-3
micro- 
10-6
nano- n
10-9
pico- p
10-12

6. How confident are we in our measurements?
Are they ACCURATE?
Are they PRECISE?
How many of the numerals in the measurement are SIGNIFICANT DIGITS?

7. Accuracy Precision Closeness of a single value to the true value
Closeness of a set of values to each other

8. Precision and Accuracy

9. Uncertainty in Measurement
All scientific measures are subject to error.
The number of digits reported reflect the accuracy of the measurement and the precision of the measuring device.
Significant Figures (Sig Figs) are all the figures known with certainty plus one extra uncertain figure.

10. Uncertainty in Measurement Instrument error
Human error
meniscus

11. Measurement on Metric Ruler
93.55 cm
97.18 cm

12. Rules: Significant Figures (Sig Figs)
All non-zero numbers are significant.
Ex) 3.45
(3 sig fig)
Zeros between non-zero numbers are significant.
Ex) 4,503
(4 sig fig)
Zeros to the left of the first non-zero digit are not significant.
Ex)
(1 sig fig)
Zeros to the right of a nonzero digit are significant IF the number contains a decimal point.
Ex) 1.90
Ex) 10,300

13. Significant Figures (Sig Figs)
1.23 grams = 3
grams = 3
2.0 grams
= 2
0.020 grams = 2
100 grams
= 1
100. grams = 3

14. How many Significant Figures
630
5020
9102
7.200 x 102

15. How many Significant Figures
630
5020
9102
7.200 x 102
Three
Two
Four

16. How many Significant Figures
5760
5002
5200
1.30 x 105

17. How many Significant Figures
5760
5002
5200
1.30 x 105
Four
Three
Two

18. > 5 round up = 5 round up < 5 round down Rounding off
If the first insignificant digit is
> 5 round up
= 5 round up
< 5 round down

19. Round off to three significant digits
546847

20. Round off to three significant digits
last significant
546847
first insignificant

21. Round off to three significant digits
Round up or
Round down

22. Round off to three significant digits
Round up
546847
546000

23. Round off to three significant digits
6876
6874
544.5
321.5

24. Round off to three significant digits
6876
6874
544.5
321.5
6880
6870
545
322

25. Scientific Notation For extremely large or small numbers Powers of 10
Ex) Speed of light is 30,000,000,000 cm/s
Move decimal to the left 10 spaces
30,000,000,000 cm/s
3 x 1010 cm/s
Ex) Wavelength of yellow light is cm
Move decimal to the right 5 spaces cm
5.9 x 10-5 cm

26. Scientific Notation Correct Scientific Notation: 5.20 x 104
Incorrect Scientific Notation: 520 x 102
Practice: Write in Scientific Notation.
6,200,000,000,000,000
6.2 x 1015
7.4 x 10-8

27. Significant Figures in Calculations
Multiplication & Division
Fewest significant digits
5.231 x 2.7 = 14
Addition & Subtraction
Least precise
= 514

28. III. Unit Conversions SI Prefix Conversions Dimensional Analysis

29. A. SI Prefix Conversions
1. Find the difference between the exponents of the two prefixes.
2. Move the decimal that many places.
To the left
or right?

30. A. SI Prefix Conversions=
532 m = _______ km
0.532
NUMBER
UNIT
NUMBER
UNIT

31. A. SI Prefix Conversions
Symbol
Factor
mega- M
106
kilo- k
103
deci- d
10-1
centi- c
10-2
move left
move right
milli- m
10-3
micro- 
10-6
nano- n
10-9
pico- p
10-12

32. A. SI Prefix Conversions
0.2
1) 20 cm = ______________ m
2) A = ______________ mA
3) 45 m = ______________ nm
4) 805 dm = ______________ km 32
45,000
0.0805

33. B. Dimensional Analysis
The “Factor-Label” Method
Units, or “labels” are canceled, or “factored” out

34. B. Dimensional Analysis
Steps:
1. Identify starting & ending units.
2. Line up conversion factors so units cancel.
3. Multiply all top numbers & divide by each bottom number.
4. Check units & answer.

35. B. Dimensional Analysis
Lining up conversion factors:
= 1
1 in = 2.54 cm
2.54 cm cm
1 =
1 in = 2.54 cm
1 in in

36. B. Dimensional Analysis
Your European hairdresser wants to cut your hair 8 cm shorter. How many inches will he be cutting off? cm in
8 cm
1 in
2.54 cm
= 3.15 in 

37. B. Dimensional Analysis
How many milliliters are in 1 quart of milk? qt mL
1 qt
1 L
1.057 qt
1000 mL
1 L
= 946 mL

38. B. Dimensional Analysis
5) Assume your mass is 55 kg. How many pounds do you weigh? kg lb
55 kg
2.2 lb
1 kg
= 121 lb

39. B. Dimensional Analysis
6) How many feet long is a 5K (5 km) race? km ft
5 km
1 mi
1.609 km
5280 ft
1 mi
= 16,408 ft

40. B. Dimensional Analysis
7) How many grams does a 10-lb. bag of potatoes weigh? lb g
10 lb
1 kg
2.2. lb
1000 g
1 kg
= 4545 g

41. B. Dimensional Analysis
8) Taft football needs 550 cm for a 1st down. How many yards is this? cm yd
550 cm
1 in
2.54 cm
1 ft
12 in
1 yd
3 ft
= 6.01 yd