Transcript Significant figures

CHAPTER 2
Analyzing Data
National Standards for Chapter 2
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UCP.1 Systems, order, and organization
UCP.2 Evidence, models, and explanation
A.1 Abilities necessary to do scientific inquiry
A.2 Understandings about scientific inquiry
B.3 Chemical reactions
B.6 Interactions of energy and matter
E.2 Understandings about science and technology
F.4 Environmental quality
F.5 Natural and human-induced hazards
G.2 Nature of scientific knowledge
G.3 Historical perspectives
Vocabulary/Study Guide
• Define each term using the Glossary
• Either write on the handout, or use your own
paper
• This is due on Test Day (tentatively, Thursday,
September 12)
Demonstration: Layers of Liquids
TITLE:
LAYERS OF LIQUIDS
OBJECTIVE:
To observe how liquids have different densities just like solids
such as lead and plastic have different densities.
PREDICTIONS: (Do not write the questions)
1.
Which solids are less dense than water?
2.
Which solids are denser than water?
3.
Which liquids are less dense than water?
4.
Which liquids are denser than water?
DATA:
Lab: Determine Density, page 39
TITLE:
DETERMINE DENSITY (Pg. 39)
OBJECTIVE:
To calculate the density of an object by finding its
mass and volume, using a scale and a graduated
cylinder.
PREDICTIONS: (Do not write the questions)
1. Why must you mass the object before immersing it in water?
2.
DATA:
Some students have tiny pieces of magnetite (dull grey) and
some students have large pieces of magnetite. Predict if they
will have the same or different densities.
Section 1: Units and Measurement
• National Standards:
– UCP.1 Systems, order, and organization
– UCP.3 Change, constancy, and measurement
– A.1 Abilities necessary to do scientific inquiry
– A.2 Understandings about scientific inquiry
– B.2 Structure and properties of matter
– G.1 Science as a human endeavor
– G.2 Nature of scientific knowledge
Objectives – Section 1
• 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.
• REVIEW VOCABULARY:
– mass: a measurement that reflects the amount of
matter an object contains
Units
• Chemists use an internationally recognized
system of units to communicate their findings.
• 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.
Base Units and SI Prefixes
Base Units and SI Prefixes
• Metric Chart
Base Units and SI Prefixes
Base Units and SI Prefixes
• 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
Base Units and SI Prefixes
• 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.
Base Units and SI Prefixes
• Metric System Handouts
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.
Derived Units
• Volume is a derived unit and is measured in
cubic meters (m3), but this is very large. A
more convenient measure is the liter, or one
cubic decimeter (dm3).
Derived Units
• Density is a derived unit, g/cm3, the amount
of mass per unit volume.
• The density equation is
density = mass/volume
Density Problems
• Example Problem #1, Page 38
• Practice Problems #1-3, Page 38
• Density Handout with Chart
Homework, Section 1
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SECTION 1 REVIEW, Page 39
Questions #4, 5, 7-10
Answer with complete sentences
Due tomorrow
Section 2: Scientific Notation and
Dimensional Analysis
• National Standards:
– UCP.1 Systems, order, and organization
– UCP.3 Change, constancy, and measurement
– A.1 Abilities necessary to do scientific inquiry
– A.2 Understandings about scientific inquiry
– E.2 Understandings about science and
technology
Objectives – Section 2
• Express numbers in scientific notation.
• Convert between units using dimensional
analysis.
• Review Vocabulary:
– quantitative data: numerical information
describing how much, how little, how big, how
tall, how fast, and so on
New Vocabulary
• scientific notation
• dimensional analysis
• conversion factor
• Scientists often express numbers in scientific
notation and solve problems using
dimensional analysis.
Scientific Notation
• Scientific notation can be used to express any
number as a number between 1 and 10
(known as the coefficient) multiplied by 10
raised to a power (known as the exponent).
– Carbon atoms in the Hope Diamond = 4.6 x 1023
– 4.6 is the coefficient and 23 is the exponent.
Scientific Notation
• Count the number of places the decimal point
must be moved to give a coefficient between 1
and 10.
• 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  102
0.0000343 = 3.43  10–5
Scientific Notation
• Practice Problems, page 41
– #11-12
– Write the problem, then the answer
– Show your work, if necessary
Scientific Notation
• Addition and subtraction
– Exponents must be the same.
– Rewrite values to make exponents the same.
– Ex. 2.840 x 1018 + 3.60 x 1017, you must rewrite one of
these numbers so their exponents are the same.
Remember that moving the decimal to the right or left
changes the exponent.
2.840 x 1018 + 0.360 x 1018
– Add or subtract coefficients.
– Ex. 2.840 x 1018 + 0.360 x 1017 = 3.2 x 1018
Scientific Notation
• Multiplication and division
– To multiply, multiply the coefficients, then add the exponents.
Ex. (4.6 x 1023)(2 x 10-23) = 9.2 x 100
– To divide, divide the coefficients, then subtract the exponent
of the divisor from the exponent of the dividend.
Ex. (9 x 107) ÷ (3 x 10-3) = 3 x 1010
Note: Any number raised to a power of 0 is equal to 1: thus, 9.2
x 100 is equal to 9.2.
Scientific Notation
• Practice Problems, page 42-43
– #13-16
– Write the problem, then the answer
– Show your work, if necessary
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.
Dimensional Analysis
• Writing conversion factors
– Conversion factors are derived from equality relationships,
such as 1 dozen eggs = 12 eggs.
– Percentages can also be used as conversion factors. They
relate the number of parts of one component to 100 total
parts.
• Practice Problems, page 45
– #17-18
– Write the problem, then the answer
– Show your work, if necessary
Dimensional Analysis
• Using conversion factors
– A conversion factor must cancel one unit and
introduce a new one.
• Practice Problems, page 45-46
– #19-23
– Write the problem, then the answer
– Show your work, if necessary
Dimensional Analysis
• Answer questions on Teaching Transparency 4
– Converting Units
Homework, Section 2
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SECTION 2 REVIEW, Page 46
Questions #24-28, 30, 31
Answer with complete sentences
Due tomorrow
Section 3: Uncertainty in Data
• National Standards:
– UCP.1 Systems, order, and organization
– UCP.3 Change, constancy, and measurement
– A.1 Abilities necessary to do scientific inquiry
– A.2 Understandings about scientific inquiry
– E.2 Understandings about science and
technology
– G.2 Nature of scientific knowledge
Objectives – Section 3
• 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.
• Review Vocabulary:
• experiment: a set of controlled observations that test
a hypothesis
New Vocabulary
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accuracy
significant figures
percent error
precision
error
• Measurements contain uncertainties that affect
how a result is presented.
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.
Accuracy and Precision
• Error is defined as the difference between an
experimental value and an accepted value.
Accuracy and Precision
• The error equation is
error = experimental value – accepted value.
• Percent error expresses error as a percentage
of the accepted value.
Accuracy and Precision
• Practice Problems, page 49
– #32-34
– Write the problem, then the answer
– Show your work, if necessary
• Teaching Transparency 5 – Precision and
Accuracy
• Problem-Solving Lab: Identify an Unknown
– Page 50
Significant Figures
• Often, precision is limited by the tools
available.
• Significant figures include all known digits
plus one estimated digit.
Significant Figures
• 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.
Significant Figures
• Practice Problems, page 51
– #35-37
– Write the problem, then the answer
– Show your work, if necessary
Problem-Solving Lab: Identify an
Unknown
• Title: Identify an Unknown, page 50
• Objective: To observe how mass and volume
data for an unknown sample be used to
identify the unknown
• Data: Calculate the volumes and density for
each of the six samples. Calculate the average
density of the six samples. Be sure to use
significant figure rules.
• Think Critically:
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.
Rounding Numbers
• 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 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 the last significant figure.
Rounding Numbers
• 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.
Rounding Numbers
• Addition and Subtraction
– Round the answer to the same number of decimal
places as the original measurement with the
fewest decimal places.
• Multiplication and Division
– Round the answer to the same number of
significant figures as the original measurement
with the fewest significant figures.
Rounding Numbers
• Practice Problems, page 53-54
– #38-44
– Write the problem, then the answer
– Show your work, if necessary
Homework, Section 3
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SECTION 3 REVIEW, Page 54
Questions #45, 47-51
Answer with complete sentences
Due tomorrow
Forensics Lab: Use Density to Date a
Coin
• Title: Use Density to Date a Coin, page 60
• Objective: To observe how density data can
be used to determine whether a penny was
minted before 1982.
• Data: Find the mass and volume for a group
of pennies. Graph your data. Calculate the
average density of each group of pennies.
• Analyze and Conclude:
Section 4: Representing Data
• National Standards:
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UCP.1 Systems, order, and organization
UCP.3 Change, constancy, and measurement
A.1 Abilities necessary to do scientific inquiry
A.2 Understandings about scientific inquiry
B.2 Structure and properties of matter
E.1 Abilities of technological design
E.2 Understandings about science and
technology
– F.1 Personal and community health
– G.2 Nature of scientific knowledge
Objectives – Section 4
• Create graphics to
reveal patterns in data
• Interpret graphs.
• Graphs visually depict
data, making it easier
to see patterns and
trends.
• Review Vocabulary:
• independent variable:
the variable that is
changed during an
experiment
• New Vocabulary:
• graph
Graphing
• A graph is a visual display of data that makes
trends easier to see than in a table.
Graphing
• A circle graph, or pie chart, has wedges that
visually represent percentages of a fixed
whole.
Graphing
• Bar graphs are often used to show how a
quantity varies across categories.
Interpreting Graphs
• Teaching Transparency 6 – Interpreting Graphs
• Math Skills Transparency 1 – Interpreting and
Drawing Graphs
Graphing
• On line graphs, independent variables are
plotted on the x-axis and dependent variables
are plotted on the y-axis.
Graphing
• If a line through the points is straight, the
relationship is linear and can be analyzed
further by examining the slope.
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.
Interpreting Graphs
• This graph shows important ozone
measurements and helps the viewer visualize
a trend from two different time periods.
Homework, Section 4
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SECTION 4 REVIEW, Page 58
Questions #52-58
Answer with complete sentences
Due tomorrow
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.
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.
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
Key Concepts
• The number of significant figures reflects the
precision of reported data.
• Calculations should be rounded to the correct
number of significant figures.
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.