1. Measurement and Calculations
Making observations is a key part of the scientific process.
Observations become more meaningful when measurements are made.

2. Two types of observations:
Qualitative (kind):
Examples: color, texture
Quantitative (amount):
Examples: mass, volume, length, density

3. A quantitative observation is called a measurement
A measurement always consists of two parts: a number and a unit

4. Scientific Notation Why?
Makes very large and very small numbers easier to use

5. Rules for Scientific Notation
Number can be represented as the product of a number between 1 and 10 and a power of 10.
Move decimal so it directly follows the first non-zero digit in the base.
Powers of 10 greater than 1 have positive exponents.
Powers of 10 less than 1 have negative exponents.

6. Example
23,500
2.35 x 104

7. Example
0.0560
5.60 x 10 -2

8. Example
25.0
2.50 x 101

9. Units
The part of a measurement called the unit tells us what scale or standard is being used.
The two most widely used systems are the English system and the metric system.

10. Commonly Used Metric Prefixes

11. SI Fundamental Units of MEASUREMENT
In 1960 an international committee of scientists met to revise the metric system.
They developed the
Systems International (SI)
Fundamental Units of Measurement.

12. They developed units that are defined by standards of measurement which are of constant value.

13. SI Fundamental Units For Chemistry
Quantity Unit Symbol
Length meter m
Mass kilogram kg
Time second s
Temperature Kelvin K
Amount mole mol
Electric current ampere amp
Luminous intensity candela can

14. Length, Volume, and Mass 1) Length SI unit is meter
1 meter = inches (about a yard)
1 inch = 2.54 centimeters
measure length using a ruler or meter stick

15. Common Metric Units for Length

16. 2) Volume
SI unit is meter3
1 dm3 = 1 L
1 cm3 = 1 mL

17. Measure volume using a
graduated cylinder

18. 3) Mass
SI unit is kilogram
Metric unit is gram
Measure mass using
a balance

20. Uncertainty in Measurement
Two kinds of numbers
1) Exact
a. counted
2 children
26 letters
b. defined
12 inches per foot
1000 g per kilogram

21. 2) Inexact Numbers
a. Measurements
Uncertainty always exists in measured quantities:
equipment limitations
skill of person taking the measurements

22. What does the pin measure?
2.84? ? ?

23. All the digits that occupy a place for which an actual measurement is made are called certain numbers
Any digit that is estimated is called an uncertain number

24. When making measurements, always record all certain numbers plus one uncertain number

25. The numbers recorded in a measurement (all the certain numbers plus one uncertain number) are called significant figures

26. Significant Figures
Significant = “measured”
Not significant = “place holder”

27. Rules for Significant Figures
1. Non-zero digits are always
significant.
1.9
= 2 sf
17.123
= 5 sf
567
= 3 sf

28. 2. Trapped zeroes are always significant.
1.01
= 3 sf
35.05
= 4 sf
300.09
= 5 sf

29. 3. Leading zeros are never
significant. =
1 sf =
3 sf

30. 4. Trailing zeros are significant only if the decimal point is present.
1.10
= 3 sf
= 4 sf
2,500
= 2 sf

31. 6.22 x 103 5. If a number is written in scientific
notation, ALL of the numbers in
the base are significant.
6.22 x 103
= 3 sf
5.000 x 104
= 4 sf

32. Rounding in Calculations
Digits less than 5 round down
Digits equal to or greater than 5 round up
In a series of calculations, don’t round until the end

34. Significant Figures in Calculations
When multiplying or dividing, the answer must have the same number of significant figures as the measurement with the fewest.

35. Example: Multiply the following
2.0 mL
3.55 mL
X 6.12 mL
2 sf
3 sf
3 sf mL
43 mL
Round answer to
2 significant figures

36. When adding or subtracting, the answer must have the same number of decimal places as the measurement with the fewest.

37. Example: Add the following
2 decimal places
0 decimal places
3 decimal places g
204 g
Round answer to 0 decimal places

38. Rounding Significant Figures
You cannot change the magnitude of the number when rounding!
Calculations cannot be more exact than the measurements on which they are based!

39. 102,433 rounded to 3 sig fig.
= 102, not 102

40. 395,952 rounded to 1 sig fig.
= 400, not 4

41. rounded to 2 sig fig.
= not

43. Dimensional Analysis
Also known as the “Factor-Label Method” or “Factoring the Units”
A systematic method for solving problems in which units are carried throughout the entire problem.

44. Using conversion factors helps ensure that answers have the proper units.

45. Examples of Conversion Factors
12 in = 1 ft
100 cm = 1 m
12 in or 1 ft
1 ft in
100cm or 1m
1 m cm

46. When determining the number of significant figures in an answer, consider only the measured digits and ignore the conversion factors.

47. Example #1
A lab bench is inches long. What is its length in feet?

48. Given: inches (4 sf)
Uknown: _____ feet
Conversion factor:
12 in or 1 ft
1 ft in

49. 175.0 in x 1 ft =
12 in
ft =
14.58 ft

50. Example #2
A marble rolled 50.0 millimeters. How many meters did it roll?

51. Given: 50.0 mm (3 sf)
? : _____m
Conversion factor:
1000 mm or 1 m
1 m mm

52. 50.0 mm x m =
1000 mm
0.05 m
.0500 m

53. Example #3
In Europe, a car was driven at 165 km/hr. What was the speed in mi/min?

54. Given: 165 km/1 hr (3 sf)
? : _____ mi/ 1 min

55. Conversion factors: 1.609 km or 1 mi 1 mi 1.609 km AND 1 hr or 60 min
60 min hr

56. 1.71 mi/min 1 hr 1.609 km 60 min 1.709136109 mi/min =
165 km x mi x 1 hr =
1 hr km min
mi/min =
1.71 mi/min

58. Heat vs. Temperature
Heat – total kinetic energy (movement) of particles in a sample.
Temperature – measurement of the average kinetic energy (speed) of the particles in a sample.

59. Question
Which would have a higher temperature, a cup of boiling hot coffee or a bathtub of warm water?

60. Answer
Boiling cup of coffee would have a higher temperature (avg. kinetic energy)

61. Question
Which would contain more heat?

62. Answer
Warm bathtub would have more heat (total kinetic energy)

63. Measuring Temperature:
Common units are
oF, oC, and K
Kelvin is used in chemistry because it starts at absolute zero which is the total absence of heat.

64. Absolute Zero – the temperature at which all molecular motion stops (the coldest temperature possible)

65. Temperature Conversions
K = °C + 273
C = K

66. Example #1:
Convert 250 Kelvin to Celsius
C = K
= C

67. Example #2:
Convert 17 0C to Kelvin
K = °C + 273
= K

68. Mass per unit volume of a material
Density
Mass per unit volume of a material
Formula: density (d) = mass (m)
volume (v)
Units: g/mL or g/cm3
Remember: 1 ml = 1 cm3

69. Rubbing Alcohol and Water
d = 0.85 g/mL
Water
d = 1.0 g/mL

70. Calculating Density
Example #1: An iron bar with a mass of 94.5 g has dimensions of 12 cm x 2.0 cm x 0.50 cm. What is its density?
(2 sf)
12 cm
2 cm
0.50 cm

71. Step 1: Calculate the volume
V = l x h x w
12 x 2.0 x .50 = 12 cm3

72. Step 2: Solve for density d = m/V 94.5 g 12 cm3 7.9 g/cm3

73. Example #2:
What volume will be occupied by an 83.5 gram sample of Gold (Au) if the density of Gold is g/mL?
(3 sf)

74. Answer
Step 1: Rearrange the density equation
d = m/V
V = m/d

75. Answer
Step 2: Solve for volume
V = m d
83.5/19.3
4.33 mL

76. Example #3: If the density of water is 1
Example #3: If the density of water is 1.0 g/mL, what is the density of 25 mL of water?
2 sf

77. Answer
d = m/v m = (d)(v) (1.0)(25) 25 g

78. Percent Error
Allows you to calculate how far off a measured value is from an accepted value.

79. Formula
% Error =
Accepted – Experimental x 100
Accepted

80. Example:
Calculate % Error if the measured value for the density of a sample of Aluminum metal (Al) is g/mL, but the accepted value is 2.7 g/mL.
2 sf

81. Answer
2.7 – 2.1 = 0.6/2.7 = .22 x 100 = 22%
If you don’t hit = (enter) before you divide, the answer will be wrong!
If you don’t hit = (enter) before you multiply, the answer will be wrong!

82. Accuracy vs. Precision Accuracy
how closely individual measurements agree with the correct or accepted value
Precision
how closely individual measurements agree with each other

83. Good precision
Good accuracy
and precision
Neither