What do you think?
•  Why use scientific notation?
•  Why are measurement units
important?
•  Why do we use significant digits?
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What do you think?
•  Why use scientific notation?
–  To more conveniently express very large
or very small numbers
•  Why are measurement units important?
–  For communication and standar
•  Why do we use significant digits?
–  To specify the precision in a measurement
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Unit Conversion
Prefixes are used to change SI units by powers
of 10, as shown in the table below.
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Unit Conversion
•  A method of treating units as algebraic
quantities, which cancel (or divide out),
is called unit conversion or
dimensional analysis.
•  For example, to convert 1.34 kg of iron
ore to grams, do as shown below:
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How long
is the
pencil?
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Significant Digits
•  We need a set of guidelines when we do
calculations so that we get rid of all those
4.243956528452940472 answers you see on
your calculator.
•  The guidelines tell us how many digits we
should round off the final answer to show the
correct precision or SIGNIFICANT DIGITS.
•  To determine the number of SIGNIFICANT (or
important) DIGITS follow several rules.
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Significant Digits
1) The numbers 1 to 9 are always significant
digits. 0 is a significant digit if it comes
between of a number between 1 and 9.
Example: 13.869 ß five significant digits
1.304 ß four significant digits.
The zero counts because it appears between
the “3” and “4”
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Significant Digits
576.00 ß five significant digits.
The zeros count because they appear
to the right of the “6” and after the
decimal.
0.08 ß one significant digit.
The zeros don’t count, because they are
to the left of the “8”.
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Significant Digits
2) When you add or subtract numbers, always check
which of the numbers is the least precise (least
numbers after the decimal). Use that many
decimals in your final answer.
Example: 11.623
2.0
+ 0.14
13.763 è round it off to 13.8, since
the number “2.0” is the least precise… it only has
one significant digit after the decimal.
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Significant Digits
3) When you multiply or divide numbers,
check which number has the fewest
significant digits. Round off your answer so
it has that many significant digits.
Ex: 4.56 x 13.8973 = 63.371688 è 63.4
We round off our final answer to three
significant digits, because “4.56” has the
fewest significant digits… three.
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What do you think?
•  Why do we make graphs?
•  What do graphs tell us that makes
their use important to data
analysis?
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Graphing Data
●  Graph the relationship between
independent and dependent variables.
●  Interpret graphs.
●  Recognize common relationships in
graphs.
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Graphing Data
Identifying Variables
A variable is any factor that might affect the
behavior of an experimental setup.
The independent variable is the factor that is
changed or manipulated during the
experiment.
The dependent variable is the factor that
depends on the independent variable.
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Graphing Data
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Graphing Data
Linear Relationships
When the line of best fit is a
straight line, as in the figure,
the dependent variable varies
linearly with the independent
variable. This relationship
between the two variables is
called a linear relationship.
The relationship can be written
as an equation.
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Graphing Data
Linear Relationships
The y-intercept, b, is the point at
which the line crosses the yaxis, and it is the y-value when
the value of x is zero.
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Graphing Data
Nonlinear Relationships
When the graph is not a straight line, it means
that the relationship between the dependent
variable and the independent variable is not
linear.
There are many types of nonlinear
relationships in science. Two of the most
common are:
•  the quadratic and
•  inverse relationships.
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Nonlinear Relationships
Quadratic Relationships
A quadratic
relationship exists
when one variable
depends on the square
of another.
A quadratic
relationship can be
represented by the
following equation:
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Nonlinear Relationships
Inverse Relationships
In an inverse
relationship, a hyperbola
results when one variable
depends on the inverse of
the other.
An inverse
relationship can be
represented by the
following equation:
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Interpreting Graphs
Making Predictions
The relationship between variables, either
represented as formulas or graphs, can be
used to predict values you have not
measured directly.
Scientists use models, including formulas
and graphs to accurately predict how
objects will behave when variables affecting
their behavior change.
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What do you think?
•  When is measurement data
precise?
•  When is measurement data
accurate?
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Precision & Accuracy
Precise - data
points are all very
close to each other.
Accurate - data
points all agree with
the true value.
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Precision & Accuracy
Example: You perform an experiment to measure the
temperature at which water boils. You set up three
containers of water and heat each one. At the
instant the water boils you measure the
temperature and get the following results:
67°C, 68°C, 68°C, 65°C, 66°C
• 
Notice these values are precise (they are almost
the same, they agree with each other), but they
are not accurate. They should be at about 100°C,
the accepted value.
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Precision & Accuracy
Example: You give someone a meter stick and
ask them “How tall is the doorway?” They
come back to you and tell you it is
1.876534693 meters high. Is it possible for
them to make a measurement like this with
a meter stick?
Nope! That’s too many decimal places! To be
that accurate you would need a laser.
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Precision & Accuracy
Remember:
As a rule of thumb, look at the smallest
unit on your measuring device. You
can probably measure to within
that…
Most rulers show millimeters. You could
safely measure something with a
regular ruler to within a millimeter.
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Precision & Accuracy
In the door example, it would be more
reasonable for the measurement to
be 187.7 cm (notice that I give the
value to within a millimeter).
And always remember to choose the
right units! Don’t measure a
person’s height in kilometers.
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