Analyzing Data
Units and
Measurements
Scientific Notation and
Dimensional Analysis
Uncertainty in Data
Representing Data
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Section 2.1 Units and Measurements
• Define SI base units for time, length, mass, and temperature.
• Explain how adding a prefix changes a unit.
• Compare the derived units for volume and density.
mass: a measurement that reflects the amount of matter an object contains
Section 2-1
Section 2.1 Units and Measurements
(cont.) base unit second meter kilogram kelvin derived unit liter density
Chemists use an internationally recognized system of units to communicate their findings.
Section 2-1
Units
• Système Internationale d'Unités (SI) is an internationally agreed upon system of measurements.
• A base unit is a defined unit in a system of measurement that is based on an object or event in the physical world, and is independent of other units.
Section 2-1
Units
(cont.)
Section 2-1
Units
(cont.)
Section 2-1
Units
(cont.)
• The SI base unit of time is the second (s), based on the frequency of radiation given off by a cesium-133 atom.
• The SI base unit for length is the meter (m), the distance light travels in a vacuum in
1/299,792,458th of a second.
• The SI base unit of mass is the kilogram
(kg), about 2.2 pounds
Section 2-1
Units
(cont.)
• The SI base unit of temperature is the kelvin (K).
• Zero kelvin is the point where there is virtually no particle motion or kinetic energy, also known as absolute zero.
• Two other temperature scales are Celsius and Fahrenheit.
Section 2-1
Derived Units
• Not all quantities can be measured with SI base units.
• A unit that is defined by a combination of base units is called a derived unit .
Section 2-1
Derived Units
(cont.)
• Volume is measured in cubic meters (m 3 ), but this is very large. A more convenient measure is the liter , or one cubic decimeter (dm 3 ).
Section 2-1
Derived Units
(cont.)
• Density is a derived unit, g/cm 3 , the amount of mass per unit volume.
• The density equation is density = mass/volume.
Section 2-1
Section 2.1 Assessment
Which of the following is a derived unit?
A.
yard
B.
second
C.
liter
D.
kilogram
A
0%
A. A
B. B
B
0%
C. C
0%
D. D
C
0%
D
Section 2-1
Section 2.1 Assessment
What is the relationship between mass and volume called?
A.
density
B.
space
C.
matter
D.
weight
A
0%
A. A
B. B
B
0%
C. C
0%
D. D
C
0%
D
Section 2-1
End of Section 2-1
Section 2.2 Scientific Notation and
Dimensional Analysis
• Express numbers in scientific notation.
• Convert between units using dimensional analysis.
quantitative data: numerical information describing how much, how little, how big, how tall, how fast, and so on
Section 2-2
Section 2.2 Scientific Notation and
Dimensional Analysis
(cont.) scientific notation dimensional analysis conversion factor
Scientists often express numbers in scientific notation and solve problems using dimensional analysis.
Section 2-2
Scientific Notation
• Scientific notation can be used to express any number as a number between
1 and 10 (the coefficient) multiplied by 10 raised to a power (the exponent).
• Count the number of places the decimal point must be moved to give a coefficient between
1 and 10.
Section 2-2
Scientific Notation
(cont.)
• The number of places moved equals the value of the exponent.
• The exponent is positive when the decimal moves to the left and negative when the decimal moves to the right.
800 = 8.0
10 2
0.0000343 = 3.43
10
–5
Section 2-2
Dimensional Analysis
• Dimensional analysis is a systematic approach to problem solving that uses conversion factors to move, or convert, from one unit to another.
• A conversion factor is a ratio of equivalent values having different units.
Section 2-2
Dimensional Analysis
(cont.)
• Using conversion factors
– A conversion factor must cancel one unit and introduce a new one.
Section 2-2
Section 2.2 Assessment
What is a systematic approach to problem solving that converts from one unit to another?
A.
conversion ratio
B.
conversion factor
C.
scientific notation
D.
dimensional analysis
A
0%
A. A
B. B
B
0%
C. C
0%
D. D
C
0%
D
Section 2-2
•
(at 3:05)
Section 2.2 Assessment
Which of the following expresses
9,640,000 in the correct scientific notation?
A.
9.64
10 4
B.
9.64
10 5
C.
9.64 × 10 6
D.
9.64
6 10
0%
A
A. A
B. B
B
0%
C. C
0%
D. D
C
0%
D
Section 2-2
Section 2.3 Uncertainty in Data
• Define and compare accuracy and precision.
• Describe the accuracy of experimental data using error and percent error.
• Apply rules for significant figures to express uncertainty in measured and calculated values.
experiment: a set of controlled observations that test a hypothesis
Section 2-3
Accuracy and Precision
• Accuracy refers to how close a measured value is to an accepted value.
• Precision refers to how close a series of measurements are to one another.
Section 2-3
Accuracy and Precision
(cont.)
• Error is defined as the difference between and experimental value and an accepted value.
Section 2-3
Accuracy and Precision
(cont.)
• The error equation is error = experimental value – accepted value.
• Percent error expresses error as a percentage of the accepted value.
Section 2-3
Significant Figures
• Often, precision is limited by the tools available.
• Significant figures include all known digits plus one estimated digit.
Section 2-3
Significant Figures
(cont.)
• Rules for significant figures
– Rule 1: Nonzero numbers are always significant.
– Rule 2: Zeros between nonzero numbers are always significant.
– Rule 3: All final zeros to the right of the decimal are significant.
– Rule 4: Placeholder zeros are not significant. To remove placeholder zeros, rewrite the number in scientific notation.
– Rule 5: Counting numbers and defined constants have an infinite number of significant figures.
Section 2-3
Rounding Numbers
• Calculators are not aware of significant figures.
• Answers should not have more significant figures than the original data with the fewest figures, and should be rounded.
Section 2-3
Rounding Numbers
(cont.)
• Rules for rounding
– Rule 1: If the digit to the right of the last significant figure is less than 5, do not change the last significant figure.
– Rule 2: If the digit to the right of the last significant figure is greater than 5, round up to the last significant figure.
– Rule 3: If the digits to the right of the last significant figure are a 5 followed by a nonzero digit, round up to the last significant figure.
Section 2-3
Rounding Numbers
(cont.)
• Rules for rounding
(cont.)
– Rule 4: If the digits to the right of the last significant figure are a 5 followed by a 0 or no other number at all, look at the last significant figure. If it is odd, round it up; if it is even, do not round up.
Section 2-3
Rounding Numbers
(cont.)
• Addition and subtraction
– Round numbers so all numbers have the same number of digits to the right of the decimal.
• Multiplication and division
– Round the answer to the same number of significant figures as the original measurement with the fewest significant figures.
Section 2-3
Section 2.3 Assessment
Determine the number of significant figures in the following:
8,200, 723.0, and 0.01.
A.
4, 4, and 3
B.
4, 3, and 3
C.
2, 3, and 1
D.
2, 4, and 1
A
0%
A. A
B. B
B
0%
C. C
0%
D. D
C
0%
D
Section 2-3
Section 2.3 Assessment
A substance has an accepted density of
2.00 g/L. You measured the density as
1.80 g/L. What is the percent error?
A.
0.20 g/L
B.
–0.20 g/L
C.
0.10 g/L
D.
0.90 g/L
A
0%
A. A
B. B
B
0%
C. C
0%
D. D
C
0%
D
Section 2-3
End of Section 2-3
Section 2.4 Representing Data
• Create graphics to reveal patterns in data.
• Interpret graphs.
independent variable: the variable that is changed during an experiment graph
Graphs visually depict data, making it easier to see patterns and trends.
Section 2-4
Graphing
• A graph is a visual display of data that makes trends easier to see than in a table.
Section 2-4
Graphing
(cont.)
• A circle graph, or pie chart, has wedges that visually represent percentages of a fixed whole.
Section 2-4
Graphing
(cont.)
• Bar graphs are often used to show how a quantity varies across categories.
Section 2-4
Graphing
(cont.)
• On line graphs, independent variables are plotted on the x -axis and dependent variables are plotted on the y -axis.
Section 2-4
Graphing
(cont.)
• If a line through the points is straight, the relationship is linear and can be analyzed further by examining the slope.
Section 2-4
Interpreting Graphs
• Interpolation is reading and estimating values falling between points on the graph.
• Extrapolation is estimating values outside the points by extending the line.
Section 2-4
Interpreting Graphs
(cont.)
• This graph shows important ozone measurements and helps the viewer visualize a trend from two different time periods.
Section 2-4
Section 2.4 Assessment
____ variables are plotted on the
____-axis in a line graph.
A.
independent, x
B.
independent, y
C.
dependent, x
D.
dependent, z
A
0%
A. A
B. B
B
0%
C. C
0%
D. D
C
0%
D
Section 2-4
Section 2.4 Assessment
What kind of graph shows how quantities vary across categories?
A.
pie charts
B.
line graphs
C.
Venn diagrams
D.
bar graphs
A
0%
A. A
B. B
B
0%
C. C
0%
D. D
C
0%
D
Section 2-4
End of Section 2-4
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Study Guide
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Section 2.1 Units and Measurements
Key Concepts
• SI measurement units allow scientists to report data to other scientists.
• Adding prefixes to SI units extends the range of possible measurements.
• To convert to Kelvin temperature, add 273 to the
Celsius temperature. K = ° C + 273
• Volume and density have derived units. Density, which is a ratio of mass to volume, can be used to identify an unknown sample of matter.
Study Guide 1
Section 2.2 Scientific Notation and
Dimensional Analysis
Key Concepts
• A number expressed in scientific notation is written as a coefficient between 1 and 10 multiplied by 10 raised to a power.
• To add or subtract numbers in scientific notation, the numbers must have the same exponent.
• To multiply or divide numbers in scientific notation, multiply or divide the coefficients and then add or subtract the exponents, respectively.
• Dimensional analysis uses conversion factors to solve problems.
Study Guide 2
Section 2.3 Uncertainty in Data
Key Concepts
• An accurate measurement is close to the accepted value. A set of precise measurements shows little variation.
• The measurement device determines the degree of precision possible.
• Error is the difference between the measured value and the accepted value. Percent error gives the percent deviation from the accepted value.
error = experimental value – accepted value
Study Guide 3
Section 2.3 Uncertainty in Data
(cont.)
Key Concepts
• The number of significant figures reflects the precision of reported data.
• Calculations should be rounded to the correct number of significant figures.
Study Guide 3
Section 2.4 Representing Data
Key Concepts
• Circle graphs show parts of a whole. Bar graphs show how a factor varies with time, location, or temperature.
• Independent ( x -axis) variables and dependent ( y -axis) variables can be related in a linear or a nonlinear manner. The slope of a straight line is defined as rise/run, or ∆ y /∆ x .
• Because line graph data are considered continuous, you can interpolate between data points or extrapolate beyond them.
Study Guide 4
Which of the following is the SI derived unit of volume?
A.
gallon
B.
quart
C.
m 3
D.
kilogram
A
0%
A. A
B. B
B
0%
C. C
0%
D. D
C
0%
D
Chapter Assessment 1
Which prefix means 1/10 th ?
A.
deci-
B.
hemi-
C.
kilo-
D.
centi-
A
0%
A. A
B. B
B
0%
C. C
0%
D. D
C
0%
D
Chapter Assessment 2
Divide 6.0
10 9 by 1.5
10 3 .
A.
4.0
10 6
B.
4.5
10 3
C.
4.0
10 3
D.
4.5
10 6
A
0%
A. A
B. B
B
0%
C. C
0%
D. D
C
0%
D
Chapter Assessment 3
Round the following to 3 significant figures 2.3450.
A.
2.35
B.
2.345
C.
2.34
D.
2.40
A
0%
A. A
B. B
B
0%
C. C
0%
D. D
C
0%
D
Chapter Assessment 4
The rise divided by the run on a line graph is the ____.
A.
x -axis
B.
slope
C.
y -axis
D.
y -intercept
A
0%
A. A
B. B
B
0%
C. C
0%
D. D
C
0%
D
Chapter Assessment 5
Which is NOT an SI base unit?
A.
meter
B.
second
C.
liter
D.
kelvin
A
0%
A. A
B. B
B
0%
C. C
0%
D. D
C
0%
D
STP 1
Which value is NOT equivalent to the others?
A.
800 m
B.
0.8 km
C.
80 dm
D.
8.0 x 10 5 cm
A
0%
A. A
B. B
B
0%
C. C
0%
D. D
C
0%
D
STP 2
Find the solution with the correct number of significant figures:
25
0.25
A.
6.25
B.
6.2
C.
6.3
D.
6.250
A
0%
A. A
B. B
B
0%
C. C
0%
D. D
C
0%
D
STP 3
How many significant figures are there in
0.0000245010 meters?
A.
4
B.
5
C.
6
D.
11
A
0%
A. A
B. B
B
0%
C. C
0%
D. D
C
0%
D
STP 4
Which is NOT a quantitative measurement of a liquid?
A.
color
B.
volume
C.
mass
D.
density
A
0%
A. A
B. B
B
0%
C. C
0%
D. D
C
0%
D
STP 5
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Table 2.2 SI Prefixes
Figure 2.10 Accuracy and Precision
CIM
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