1. The SI System of Measurement (le Système International, SI)

2. The Nature of Measurement
A Measurement is a quantitative observation consisting of TWO parts
Part 1 - number
Part 2 - scale (unit)
Examples:
20 grams
6.63 x Joule·seconds

3. The Fundamental SI Units (le Système International, SI)

5. King Henry Died Unexpectedly Drinking Chocolate Milk
K H D U D C M m n

6. Metric Conversions g m L 103 102 101 10-1 10-2 10-3 kilo hecto deka
Base
unit
deci
centi
milli
Conversions in the metric system are merely a matter of moving a decimal point. The “base unit” means the you have a quantity (grams, meters, Liters, etc without a prefix.

7. Metric Conversions g m L 103 102 101 10-1 10-2 10-3 kilo hecto deka
Base
unit
deci
centi
milli 1 2 3
18. L
18. liters = 18,000. mL
Example #1: Convert 18 liters to milliliters

8. Metric Conversions g m L 103 102 101 10-1 10-2 10-3 kilo hecto deka
Base
unit
deci
centi
milli 3 2 1
450. mg = g
450.mg
Example #2: Convert 450 milligrams to grams

9. Metric Conversions g m L 103 102 101 10-1 10-2 10-3 kilo hecto deka
Base
unit
deci
centi
milli 1 2 3 4 5 6
20 kg
20 kg = 20,000,000 mg
Example #3: Convert 20 kilograms to milligrams

10. Uncertainty and Significant Figures
Cartoon courtesy of Lab-initio.com

11. Uncertainty in Measurement
A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.

12. Accuracy – how close a measurement is to the true value
Precision – A) how close a set of measurements are to each other
B) the detail of a number (for example, 3.00 g is more
precise than 3 g)
accurate
&
precise
precise
but
not accurate
not accurate
&
not precise
1.8

13. Chemistry In Action
On 9/23/99, $125,000,000 Mars Climate Orbiter entered Mars’ atmosphere 100 km lower than planned and was destroyed by heat.
1 lb = 1 N
1 lb = 4.45 N
“This is going to be the cautionary tale that will be embedded into introduction to the metric system in elementary school, high school, and college science courses till the end of time.”
One team used English units (e.g., inches, feet and pounds) while the other used metric units for a key spacecraft operation.
1.7

14. Significant Figures ~Fast fingers~

15. Rules for Counting Significant Figures (SigFigs)- Details
Nonzero integers always count as significant figures.
3456 has
4 significant figures

16. 0.0486 has 3 significant figures 0.00000486 has
SigFigs – ZERO Details
Leading zeros never count as
significant figures.
has
3 significant figures
has

17. 16.07 has 4 significant figures
SigFigs – ZERO Details
Captive zeros always count as significant figures.
16.07 has
4 significant figures

18. 9.300 has 4 significant figures 2500 has 2 significant figures
SigFigs – ZERO Details
Trailing zeros are significant only if the number has a decimal point
9.300 has
4 significant figures
2500 has
2 significant figures

19. 1 inch = 2.54 cm, exactly SigFigs 8 apples
Exact numbers & equivalent statements have an infinite number of significant figures.
8 apples
1 inch = cm,
exactly

20. Can you summarize the rules for SigFigs?

21. Sig Fig Practice #1
How many significant figures are in each of the following measurements?
24 mL
2 significant figures
3001 g
4 significant figures m3
3 significant figures
6.4 x 104 molecules
2 significant figures
560 kg
2 significant figures
1.8

22. Sig Fig Practice #2 1.0070 m  5 sig figs 17.10 kg  4 sig figs
How many significant figures in each of the following?
m 
5 sig figs
17.10 kg 
4 sig figs
100,890 L 
5 sig figs
3.29 x 103 s 
3 sig figs
cm 
2 sig figs
3,200,000 ns
2 sig figs

23. Decimal Places

24. Significant Figures – Mathematical Operation Rules
for Addition or Subtraction
The answer cannot have more digits to the right of the decimal
point than any of the original numbers. (Answer must match the
least precise number in the question.)
89.332
1.1 +
90.432
Shows the thousandths place
Only shows the tenth place
Answer must match the least precise used, so
round off to the tenth place:
3.70
0.7867
Shows the hundredth place
Shows the ten thousandths place
Answer must match the least precise used, so
round off to the hundredth place: 0.79
1.8

25. Significant Figures - Mathematical Operation Rules
for Multiplication or Division
The number of significant figures in the result is set by the original number that has the smallest number of significant figures. (The answer must match the least # of sigfigs in the question.)
4.51 x =
= 16.5
3 sig figs
round to
3 sig figs
5 sig figs
6.8 ÷ =
= 0.061
2 sig figs
round to
2 sig figs
5 sig figs
1.8

26. Rules for Significant Figures in Mathematical Operations
Multiplication and Division:
Number of sig figs in the result
equals the number in the least precise
measurement used in the calculation.
6.38 x 2.0 =
= 12.76
rounded to correct # of sigfigs:
13 (2 sig figs)

27. Sig Fig Practice #3 Calculation Calculator says: Answer 3.24 m x 7.0 m
100.0 g ÷ 23.7 cm3
g/cm3
4.22 g/cm3
0.02 cm x cm
cm2
0.05 cm2
710 m ÷ 3.0 s
m/s
240 m/s
lb x 3.23 ft
lb·ft
5870 lb·ft
1.030 g ÷ 2.87 mL
g/mL
2.96 g/mL

28. Sig Fig Practice #3 Calculation Calculator says: Answer 3.24 m + 7.0 m
100.0 g g
76.27 g
76.3 g
0.02 cm cm
2.391 cm
2.39 cm
713.1 L L L
709.2 L
lb lb lb lb
2.030 mL mL
0.16 mL
0.160 mL

29. Significant Figures Exact Numbers
Numbers from definitions or numbers of objects are considered
to have an infinite number of significant figures. (They will not
Limit the number of sigfigs in our answer.)
The average of three measured lengths; 6.64, 6.68 and 6.70? 3
= = 6.67
= 7
Because 3 is an exact number
1.8

30. Dimensional Analysis Method of Solving Problems
Determine which unit conversion factor(s) are needed
Carry units through calculation
If all units cancel except for the desired unit(s), then the problem was solved correctly.
Round to proper number of sigfigs.
How many mL are in L?
1 L = 1000 mL (this statement has infinite sigfigs!) 1L
1000 mL
1.632 L x
= 1632 mL 1L
1000 mL
1.632 L x = L2 mL
1.9

31. Dimensional Analysis Method of Solving Problems
Determine which unit conversion factor(s) are needed
Carry units through calculation
If all units cancel except for the desired unit(s), then the problem was solved correctly.
Round to proper number of sigfigs.
How many g are in 355 kg?
1 kg = 1000 g (this statement has infinite sigfigs!)
1kg
1000 g
355 kg x
= g
1.9

32. The speed of sound in air is about 343 m/s
The speed of sound in air is about 343 m/s. What is this speed in miles per hour?
meters to miles
seconds to hours
1 mi = 1609 m
EXACTLY
1 min = 60 s
EXACTLY
1 hour = 60 min
EXACTLY
343 m s x
1 mi
1609 m
60 s
1 min x
60 min
1 hour x
= 767 mi
hour
Determine which unit conversion factor(s) are needed
Carry units through calculation
If all units cancel except for the desired unit(s), then the problem was solved correctly.
Round to proper number of sigfigs.
1.9

33. SCIENTIFIC NOTATION

34. Scientific Notation In science, we deal with some very LARGE numbers:
1 mole = atoms
In science, we deal with some very SMALL numbers:
Mass of an electron = kg

35. Imagine the difficulty of calculating the mass of 1 mole of electrons!kg
x atoms
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36. (Positive or negative)
Scientific Notation:
A method of representing very large or very small numbers in the form:
M x 10n
n is an integer
(Positive or negative)
1  M  10

37. . 9 8 7 6 5 4 3 2 1
Step #1: Insert an understood decimal point
Step #2: Decide where the decimal must end
up so that one number is to its left
Step #3: Count how many places you bounce
the decimal point
Step #4: Re-write in the form M x 10n

38.
2.5 x 109
The exponent is positive because the decimal form of the number we started with was greater than 1.

39. 0.0000579 1 2 3 4 5 Step #2: Decide where the decimal must end
up so that one number is to its left
Step #3: Count how many places you bounce
the decimal point
Step #4: Re-write in the form M x 10n

40.
5.79 x 10-5
The exponent is negative because the decimal form of the number we started with was less than 1.

41. (Positive or negative)
Scientific notation expresses a number in the form:
M x 10n
n is an integer
(Positive or negative)
1  M  10

42. Metric Conversion Practiceg m L
103
102
101
10-1
10-2
10-3
kilo
hecto
deka
Base
unit
deci
milli
centi
Liters
103
102
101
10-1
10-2
10-3 kL hL
daL L
Base
Unit dL mL cL

43. Problem #1 Convert 400 mL to Liters 400 mL 1 L .400 L = 1 000 mL
10-1
10-2
10-3
101
102
103
Base
unit
deci
centi
milli
deka
hecto
kilo
= 4x10-1 L

44. Problem #2 Convert 10 meters to mm 10 m 1 000 mm 10 000 mm = 1 m
= 1x104 mm
10-1
10-2
10-3
101
102
103
Base
unit
deci
centi
milli
deka
hecto
kilo

45. Problem #3 Convert 73 grams to kg 73 g 1 kg 0.073 kg = 1 000 g
= 7.3x10-2 kg
10-1
10-2
10-3
101
102
103
Base
unit
deci
centi
milli
deka
hecto
kilo

46. Problem #4 Convert 0.02 kilometers to m 0.02 km 1 000 m 20 m = 1 km
= 2x101 m
10-1
10-2
10-3
101
102
103
Base
unit
deci
centi
milli
deka
hecto
kilo

47. Problem #5 Convert 20 centimeters to m 20 cm 1 m 0.2 m = 100 cm
= 2x10-1 m
10-1
10-2
10-3
101
102
103
Base
unit
deci
centi
milli
deka
hecto
kilo

48. Problem #6 Convert 450 milliliters to dL 450 mL 1 dL 4.5 dL = 100 mL
= 4.5x100 dL
10-1
10-2
10-3
101
102
103
Base
unit
deci
centi
milli
deka
hecto
kilo

49. Problem #7 Convert 10 kilograms to grams 10 kg 1 000 g 10 000 g = 1 kg
= 1x104 g
10-1
10-2
10-3
101
102
103
Base
unit
deci
centi
milli
deka
hecto
kilo

50. Problem #8 Convert 935 mg to cg 1 935 mg cg 93.5 cg = 10 mg
10-1
10-2
10-3
101
102
103
Base
unit
deci
centi
milli
deka
hecto
kilo
= 9.35x101 cg

51. Problem #9 Convert 5.2 kg to mg 5.2 kg 1 000 000 mg mg = 1 kg
10-1
10-2
10-3
101
102
103
Base
unit
deci
centi
milli
deka
hecto
kilo
= mg
= 5.2x106 mg

52. Problem #10 Convert 175 mL to kL 1 kL 175 mL = kL 1000000 mL = kL mL
10-1
10-2
10-3
101
102
103
Base
unit
deci
centi
milli
deka
hecto
kilo
= 1.75x10-4 kL

53. Problem #11 Convert 288 g to mg 1000 mg 288 g = mg 1 g = 2.88 x105 mg
288000 = mg 1 g
10-1
10-2
10-3
101
102
103
Base
unit
deci
centi
milli
deka
hecto
kilo
= 2.88 x105 mg

54. Tonight’s Homework
1) Finish worksheets from today. Glue into notebook. 2) Read the entire Metric Lab Packet and come prepared to begin the lab.

55. VI. Derived SI units
derived unit--a unit that can be obtained from combinations of fundamental units.

56. Draw a picture of a cube that is 1 cm x 1 cm x 1 cm below:
What is the volume of this box? 1 cm3 If you fill the box with water, what is the volume of the water? 1 mL
1 cm
1 cm
1 cm

57. Milliliter (mL): 1 mL = 1 cm3 = 1 cc
What’s cc mean?
Cubic centimeter

58. Density
Density—the ratio that compares the mass of the substance to its volume

59. Commonly used units are solid: g/cm3 liquid: g/mL gas: g/L
d = m/v
Commonly used units are
solid:
g/cm3
liquid:
g/mL
gas:
g/L

60. Example 36: Find the density of a piece of Al with a volume of 4
Example 36: Find the density of a piece of Al with a volume of 4.0 cm3 and a mass of 10.8 g.  
d = m/v
d = 10.8 g/ 4.0 cm3
(yes, you must show units in your work)
2.7 g/cm3

61. Example 37: A 40. 0 cm3 sample of quartz has a density of 2. 65 g/cm3
Example 37: A 40.0 cm3 sample of quartz has a density of 2.65 g/cm3. What is the mass of the quartz sample?  
d = m/v
Rearrange your equation first!
m = d x v
m = 2.65 g/cm3 x 40.0 cm3
m = 106 g

62. Example 38: The density of a sample of cork is 0. 24 g/cm3
Example 38: The density of a sample of cork is 0.24 g/cm3. What is the volume of this sample if it has a mass of 36.2 g?  
d = m/v
Rearrange equation!
v = m/d
v = __36.2 g_
0.24 g/cm3
V = 150 cm3 (2 sigfigs!)

63. Diagram: Now, draw that picture of a cube that is 1 cm x 1 cm x 1 cm again.
What is the volume of this box? 1 cm3 or 1 mL If you fill the box with water, what is the MASS of the water? 1 g
1 cm
1 cm

64. What’s it’s mass if it were filled with aluminum. 2. 7 g gold. 19
What’s it’s mass if it were filled with aluminum? 2.7 g gold?? 19.3 g Air? g Wood? 0.9 g
1 cm
1 cm
1 cm

65. Important fact to memorize!
The density of water is
1 g/mL

66. WATER AND DENSITY 10 g 25 mL Water has a density of ~1 g/mL.
1 mL of water has a mass of 1 gram.
Mass of 10 mL of water?
10 g
Volume of 25 g of water?
25 mL
Water is densest at 4ºC, therefore, ice floats.