1. Section 2.1 Units and Measurements
Pages 32-39

2. International System of Units (SI System)
In 1960, the metric system was standardized in the form of the International System of Units (SI). These SI units were accepted by the international scientific community as the system for measuring all quantities.

3. SI Base Units are defined by an object or event in the physical world.
The foundation of the SI is seven independent quantities
and their SI base units. You must learn the first 5
quantities listed!
Quantity
Base Unit
Time
second (s)
Length
meter (m)
Mass
kilogram (kg)
Temperature
Kelvin (K)
Amount of a Substance
mole (mol)
Electric Current
ampere (A)
Luminous Intensity
candela (cd)

4. SI Prefixes Prefix Symbol Numerical Value Power of 10 Mega M 1,000,000
SI base units are not always convenient to use so prefixes are attached to the base unit, creating a more convenient easier-to-use unit. You must memorize these!
Prefix
Symbol
Numerical Value
Power of 10
Mega M
1,000,000
106
Kilo k
1000
103
---- 1
100
Deci d
0.1
10-1
Centi c
0.01
10-2
Milli m
0.001
10-3
Micro u
10-6
Nano n
10-9
Pico P
10-12

5. Temperature The Fahrenheit scale is not used in chemistry.
Temperature is a measure of the average kinetic energy of the particles in a sample of matter.
The Fahrenheit scale is not used in chemistry.

6. SI Derived Units 1 cm3 = 1 mL 1 dm3 = 1 L Volume (m3 or dm3 or cm3 )
In addition to the seven base units, other SI units can be made from combinations of the base units.
Area, volume, and density are examples of derived units.
Volume (m3 or dm3 or cm3 )
length  length  length
1 cm3 = 1 mL
1 dm3 = 1 L

7. m V D = Density m = mass V = volume
Density (kg/m3 or g/cm3 or g/mL) is a physical property of matter.
D = m V
m = mass
V = volume

8. Density V = 825 cm3 m = DV D = 13.6 g/cm3 m = (13.6 g/cm3)(825cm3)
An object has a volume of 825 cm3 and a density of 13.6 g/cm3. Find its mass.
GIVEN:
V = 825 cm3
D = 13.6 g/cm3
m = ?
WORK:
m = DV
m = (13.6 g/cm3)(825cm3)
m = 11,220 g
m = 11,200 g (correct sig figs)

9. Density D = 0.87 g/mL V = m V = ? m = 25 g V = 25 g 0.87 g/mL
A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid?
GIVEN:
D = 0.87 g/mL
V = ?
m = 25 g
WORK:
V = m D
V = 25 g
0.87 g/mL
= mL
V = 29 mL (correct sig figs)

10. Non SI Units
The volume unit, liter (L), and temperature unit, Celsius (C), are examples of non-SI units frequently used in chemistry.

11. SI & English Relationships
One meter is approximately 3.3 feet.
One kilogram weighs approximately 2.2 pounds at the surface of the earth.
Remember: Mass (amount of material in the object) is constant,but weight (force of gravity on the object) may change.
One liter or one dm3 is slightly more than a quart, 1.06 quart to be exact.

12. Section 2.2 Scientific Notation
Pages 40-43

13. Scientific Notation

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

15. Imagine the difficulty of calculating the mass of 1 mole of electrons!kg x
???????????????????????????????????

16. Scientific Notation:
A method of representing very large or very small numbers in the form:
M x 10n
M is a number between 1 and 10
n is an integer

17. . 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

18. 2.5 x 109
The exponent is the number of places we moved the decimal.

19. 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

20. 5.79 x 10-5
The exponent is negative because the number we started with was less than 1.

21. PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION
ADDITION AND SUBTRACTION

22. Review: M x 10n Scientific notation expresses a number in the form:
n is an integer
1  M  10

23. IF the exponents are the same, we simply add or subtract the numbers in front and bring the exponent down unchanged.
4 x 106
+ 3 x 106 7
x 106

24. The same holds true for subtraction in scientific notation.
4 x 106
- 3 x 106 1
x 106

25. If the exponents are NOT the same, we must move a decimal to make them the same.

26. 4.00 x 106
4.00 x 106
x 105
+ .30 x 106
4.30
x 106
Move the decimal on the smaller number!

27. A Problem for you…
2.37 x 10-6
x 10-4

28. Solution…
x 10-6
2.37 x 10-6
x 10-4

29. Solution…
x 10-4
x 10-4
x 10-4

30. PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION
Multiplication and Division

31. Multiplication
4.0 x 106
Exponents do NOT have to be the same. MULTIPLY the coefficients and then ADD the exponents.
X 3.0 x 105
12 x 1011
1.2 x 1012
Rewrite in proper
scientific notation.

32. Division
4.0 x 106
Exponents do NOT have to be the same. DIVIDE the coefficients and then SUBTRACT the exponents.
÷ 3.0 x 105
1.3 x 101

33. Section 2.2 Dimensional Analysis
Pages 44-46

34. Dimensional Analysis Dimensional Analysis
A tool often used in science for converting units within a measurement system
Conversion Factor
A numerical factor by which a quantity expressed in one system of units may be converted to another system

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

36. Dimensional Analysis Steps to solving problems:
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.

37. Conversion Factors
Fractions in which the numerator and denominator are EQUAL quantities expressed in different units
Example: in. = 2.54 cm
Factors: 1 in and cm
2.54 cm in.

38. How many minutes are in 2.5 hours?
conversion factor
cancel
2.5 hr 1 x
60 min
1 hr
= 150 min
By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers!

39. Convert 400 mL to Liters
400 mL 1 L
.400 L =
1000 mL
= 0.4 L
= 4x10-1 L

40. Convert 0.02 kilometers to m
0.02 km
1 000 m 20 m = 1 km
= 2x101 m

41. Squared and Cubed Conversions
Convert cm3 to dm3.
1dm=10cm

42. Multiple Unit Conversions
Convert 568 mg/dL to g/L.
1 g = 1000 mg
1L = 10 dL

43. Section 2.3 Uncertainty in Data
Pages 47-49

44. Types of Observations and Measurements
We make QUALITATIVE observations of reactions — changes in color and physical state.
We also make QUANTITATIVE MEASUREMENTS, which involve numbers.

45. Nature of Measurement
Measurement – quantitative observation consisting of two parts:
Number
Scale (unit)
Examples:
20 grams
6.63 × joule·seconds

46. Accuracy vs. Precision ACCURATE = CORRECT PRECISE = CONSISTENT
Accuracy - how close a measurement is to the accepted value
Precision - how close a series of measurements are to each other
ACCURATE = CORRECT
PRECISE = CONSISTENT

47. Accuracy vs. Precision

48. Precision and Accuracy in Measurements
In the real world, we never know whether the measurement we make is accurate
We make repeated measurements, and strive for precision
We hope (not always correctly) that good precision implies good accuracy

49. Percent Error your value given value
Indicates accuracy of a measurement
your value
given value

50. Percent Error
A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL.
(correct sig figs)

51. Section 2.3 Significant Figures or Digits
Pages 50-54

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

53. Why Is there Uncertainty?
Measurements are performed with instruments
No instrument can read to an infinite number of decimal places

54. Significant Figures 2.31 cm Indicate precision of a measurement.
Recording Sig Figs
Sig figs in a measurement include the known digits plus a final estimated digit
2.31 cm

55. Significant Figures
What is the length of the cylinder?

56. Significant figures The cylinder is 6.3 cm…plus a little more
The next digit is uncertain; 6.36? 6.37?
We use three significant figures to express the length of the cylinder.

57. When you are given a measurement to work with in a chemistry problem you may not know the type of instrument that was used to make the measurement so you must apply a set of rules in order to determine the number of significant digits that are in the measurement.

58. Rules for Counting Significant Figures
Nonzero integers always count as significant figures.
3456 has
4 significant figures

59. Rules for Counting Significant Figures
Zeros
- Leading zeros do not count as
significant figures.
has
3 significant figures

60. Rules for Counting Significant Figures
Zeros
- Captive zeros always count as
significant figures.
16.07 has
4 significant figures

61. Rules for Counting Significant Figures
Zeros
Trailing zeros are significant only if the number contains a decimal point.
9.300 has
4 significant figures
9,300 has
2 significant figures

62. Rules for Counting Significant Figures
Exact Numbers do not limit the # of sig figs in the answer. They have an infinite number of sig figs.
Counting numbers: 12 students
Exact conversions: 1 m = 100 cm
“1” in any conversion: 1 in = 2.54 cm

63. Sig Fig Practice #1 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 
2 sig figs

64. Significant Numbers in Calculations
A calculated answer cannot be more precise than the measuring tool.
A calculated answer must match the least precise measurement.
Significant figures are needed for final answers from
1) multiplying or dividing
2) adding or subtracting

65. Rules for Significant Figures in Mathematical Operations
Multiplication and Division
Use the same number of significant figures in the result as the data with the fewest significant figures.
1.827 m x m = m2 (calculator)
= 1.39 m2 (three sig. fig.)
453.6 g / 21 people = 21.6 g/person (calculator)
= g/person (four sig. fig.)
(Question: why didn’t we round to 22 g/person?)

66. Rounding Numbers in Chemistry
If the digit to the right of the last sig fig is less than 5, do not change the last sig fig.
 2.53
If the digit to the right of the last sig fig is greater than 5, round up the last sig fig.
 2.54
If the digit to the right of the last sig fig is a 5 followed by a nonzero digit, round up the last sig fig 
If the digit to the right of the last sig fig is a 5 followed by zero or no other number, look at the last sig fig. If it is odd round it up; if it is even do not round up  2.54
 2.52

67. Sig Fig Practice #2 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

68. Rules for Significant Figures in Mathematical Operations
Addition and Subtraction: The number of decimal places in the result equals the number of decimal places in the least precise measurement. Use the same number of decimal places in the result as the data with the fewest decimal places.
m m – m = ?
= m (calculator)
= m (2 decimal places)

69. Adding and Subtracting with Trailing Zeros
The answer has the same number of trailing zeros as the measurement with the greatest number of trailing zeros.
110 one trailing zero
two trailing zeros
2840.3
answer 2800 two trailing zeros

70. 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
g g g g
2.030 mL mL
0.16 mL
0.160 mL

71. Learning Check A. Which answers 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

72. Learning Check 2) 400.0 and 40 3) 0.000015 and 150,000
In which set(s) do both numbers contain the same number of significant figures?
1) and 22.00
2) and 40
3) and 150,000

73. Learning Check
In each calculation, round the answer to the correct number of significant figures.
A =
1) ) ) 257
B =
1) ) ) 40.7

74. Learning Check A. 2.19 X 4.2 = 1) 9 2) 9.2 3) 9.198 B. 4.311 ÷ 0.07 =
1) ) )
B ÷ =
1) ) ) 60
C X =
X 0.060
1) ) )