Measurements and Their Uncertainty 3.1
3.1
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Using and Expressing
Measurements
Bell Work
What are some examples from the
“Real World” of when you would
need to take scientific
measurements?
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Using and Expressing
Measurements
A measurement is a quantity that has both a
number and a unit.
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Measurements and Their
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Using and Expressing
Measurements
scientific notation: a
coefficient and 10 raised to
a power.
The number of stars in a
galaxy is an example of an
estimate that should be
expressed in scientific
notation. Why?
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3.1
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Uncertainty
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Accuracy, Precision, and Error
Accuracy and Precision
• Accuracy is a measure of how close a
measurement comes to the actual or true
value of whatever is measured.
• To evaluate the accuracy of a measurement,
the measured value must be compared to
the correct value.
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Measurements and Their
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Precision is a measure of how close a
series of measurements are to one another.
To evaluate the precision of a measurement, you must
compare the values of two or more repeated
measurements.
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Measurements and Their
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Accuracy, Precision, and Error
Just because a measuring device works, you
cannot assume it is accurate. The scale below
has not been properly zeroed, so the reading
obtained for the person’s weight is inaccurate.
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Accuracy, Precision, and Error
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Accuracy, Precision, and Error
Determining Error
• The accepted value is the correct value
based on reliable references.
• The experimental value is the value
measured in the lab.
• The difference between the experimental
value and the accepted value is called the
error.
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Measurements and Their
Uncertainty
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Accuracy, Precision, and Error
The percent error is the absolute value of the
error divided by the accepted value, multiplied
by 100%.
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Accuracy, Precision, and Error
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Measurements and Their
Uncertainty
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Sig Figs
The significant figures in a measurement include
all of the digits that are known, plus a last digit that
is estimated.
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Significant Figures in Measurements
Significant Figures in Measurements
Why must measurements be
reported to the correct number of
significant figures?
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3.1
Measurements and Their
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Significant Figures in Measurements
Example:
Suppose you estimate a weight that is between
2.4 lb and 2.5 lb to be 2.46 lb. The first two
digits (2 and 4) are known. The last digit (6) is
an estimate and involves some uncertainty. All
three digits convey useful information, however,
and are called significant figures.
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Significant Figures in Measurements
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Significant Figures in Measurements
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Measurements and Their
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Significant Figures in Measurements
Animation 2
See how the precision of a calculated result
depends on the sensitivity of the measuring
instruments.
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Measurements and Their
Uncertainty
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Significant Figures in Measurements
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Practice Problems for Conceptual Problem 3.1
Problem Solving 3.2 Solve Problem 2
with the help of an interactive guided
tutorial.
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Significant Figures in Calculations
Significant Figures in Calculations
How does the precision of a
calculated answer compare to the
precision of the measurements used
to obtain it?
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Measurements and Their
Uncertainty
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Significant Figures in Calculations
A calculated answer cannot be more
precise than the least precise
measurement from which it was
calculated.
The calculated value must be rounded to
make it consistent with the measurements
from which it was calculated.
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Measurements and Their
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Significant Figures in Calculations
Rounding
To round a number, you must first decide how
many significant figures your answer should
have. The answer depends on the given
measurements and on the mathematical
process used to arrive at the answer.
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SAMPLE PROBLEM 3.1
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SAMPLE PROBLEM 3.1
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SAMPLE PROBLEM 3.1
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Practice Problems for Sample Problem 3.1
Problem Solving 3.3 Solve Problem 3
with the help of an interactive guided
tutorial.
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Significant Figures in Calculations
Addition and Subtraction
The answer to an addition or subtraction
calculation should be rounded to the same
number of decimal places (not digits) as the
measurement with the least number of decimal
places.
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SAMPLE PROBLEM 3.2
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SAMPLE PROBLEM 3.2
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SAMPLE PROBLEM 3.2
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Practice Problems for Sample Problem 3.2
Problem Solving 3.6 Solve Problem 6
with the help of an interactive guided
tutorial.
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Significant Figures in Calculations
Multiplication and Division
• In calculations involving multiplication and
division, you need to round the answer to the
same number of significant figures as the
measurement with the least number of
significant figures.
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SAMPLE PROBLEM 3.3
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SAMPLE PROBLEM 3.3
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Practice Problems
for Sample Problem 3.3
Problem Solving 3.8 Solve
Problem 8 with the help of an
interactive guided tutorial.
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Section Assessment
Assess students’ understanding
of the concepts in Section 3.1.
Continue to:
-or-
Launch:
Section Quiz
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3.1 Section Quiz
1. In which of the following expressions is the
number on the left NOT equal to the number
on the right?
a. 0.00456  10–8 = 4.56  10–11
b. 454  10–8 = 4.54  10–6
c. 842.6  104 = 8.426  106
d. 0.00452  106 = 4.52  109
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3.1 Section Quiz
2. Which set of measurements of a 2.00-g
standard is the most precise?
a. 2.00 g, 2.01 g, 1.98 g
b. 2.10 g, 2.00 g, 2.20 g
c. 2.02 g, 2.03 g, 2.04 g
d. 1.50 g, 2.00 g, 2.50 g
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3.1 Section Quiz
3. A student reports the volume of a liquid as
0.0130 L. How many significant figures are in
this measurement?
a. 2
b. 3
c. 4
d. 5
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