Transcript Power Point 3.1
3.1
Measurements and Their Uncertainty 3.1
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3.1
Measurements and Their Uncertainty > 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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3.1
Measurements and Their Uncertainty > Using and Expressing Measurements
A
measurement
is a quantity that has both a number and a unit. © Copyright Pearson Prentice Hall
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3.1
Measurements and Their Uncertainty > 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
Measurements and Their Uncertainty > 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 Uncertainty > 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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3.1
Measurements and Their Uncertainty > 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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3.1
Measurements and Their Uncertainty > Accuracy, Precision, and Error
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3.1
Measurements and Their Uncertainty > Accuracy, Precision, and Error Determining Error
• The
accepted value
is the correct value based on reliable references. • The
experimental value
measured in the lab. is the value • The difference between the experimental value and the accepted value is called the
error
.
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3.1
Measurements and Their Uncertainty > 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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3.1
Measurements and Their Uncertainty > Accuracy, Precision, and Error
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Measurements and Their Uncertainty > Sig Figs
The
significant figures
all of the digits that are known, plus a last digit that is estimated.
in a measurement include
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3.1
Measurements and Their Uncertainty > 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 Uncertainty > 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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3.1
Measurements and Their Uncertainty > Significant Figures in Measurements
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3.1
Measurements and Their Uncertainty > Significant Figures in Measurements
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Measurements and Their Uncertainty > 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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3.1
Measurements and Their Uncertainty > 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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3.1
Measurements and Their Uncertainty > 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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3.1
Measurements and Their Uncertainty > 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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3.1
Measurements and Their Uncertainty > 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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3.1
Measurements and Their Uncertainty > 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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3.1
Measurements and Their Uncertainty > 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: Launch:
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Section Quiz Slide 38 of 48
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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 10 4 = 8.426 10 6 d. 0.00452 10 6 = 4.52 10 9
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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 © Copyright Pearson Prentice Hall
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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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