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© Copyright Pearson Prentice Hall
Measurements and Their Uncertainty
>
Slide 2 of 48
Using and Expressing Measurements
Using and Expressing Measurements
How do measurements relate to science?
3.1
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Measurements and Their Uncertainty
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Slide 3 of 48
3.1 Using and Expressing Measurements
A measurement is a quantity that has both a number and a unit.
It is important to make measurements and to decide whether a measurement is correct.
© Copyright Pearson Prentice Hall
Measurements and Their Uncertainty
>
Slide 4 of 48
3.1 Using and Expressing Measurements
In scientific notation, a given number is written as the product of two numbers: 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.
© Copyright Pearson Prentice Hall
Measurements and Their Uncertainty
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Slide 5 of 48
Accuracy, Precision, and Error
Accuracy, Precision, and Error
How do you evaluate accuracy and precision?
3.1
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Measurements and Their Uncertainty
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Slide 6 of 48
3.1 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.
• Precision is a measure of how close a series of measurements are to one another.
© Copyright Pearson Prentice Hall
Measurements and Their Uncertainty
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Slide 7 of 48
3.1 Accuracy, Precision, and Error
To evaluate the accuracy of a measurement, the measured value must be compared to the correct value.
To evaluate the precision of a measurement, you must compare the values of two or more repeated measurements.
© Copyright Pearson Prentice Hall
Measurements and Their Uncertainty
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Slide 8 of 48
3.1 Accuracy, Precision, and Error
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Measurements and Their Uncertainty
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Slide 9 of 48
3.1 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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Slide 10 of 48
3.1 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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Measurements and Their Uncertainty
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Slide 11 of 48
Accuracy, Precision, and Error3.1
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Measurements and Their Uncertainty
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Slide 12 of 48
3.1 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.
© Copyright Pearson Prentice Hall
Measurements and Their Uncertainty
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Slide 13 of 48
Significant Figures in Measurements
Significant Figures in Measurements
Why must measurements be reported to the correct number of significant figures?
3.1
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Measurements and Their Uncertainty
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Slide 14 of 48
Significant Figures in Measurements
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.
The significant figures in a measurement include all of the digits that are known, plus a last digit that is estimated.
3.1
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Measurements and Their Uncertainty
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Slide 15 of 48
Significant Figures in Measurements
The calculated answers often depend on the number of significant figures in the values used in the calculation.
3.1
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Measurements and Their Uncertainty
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Slide 16 of 48
Significant Figures in Measurements3.1
Rules for determining significant figures:
1.) Every nonzero digit in a measurement is
significant.
examples: all these measurements have 3
significant figures in them:
24.7 meters
0.743 meter
714 meters
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Measurements and Their Uncertainty
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Slide 17 of 48
Significant Figures in Measurements3.1
2.) Zeros appearing between nonzero digits are significant.
examples: These have 4 in them:
7003 meters
40.79 meters
1.503 meters
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Measurements and Their Uncertainty
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Slide 18 of 48
Significant Figures in Measurements3.1
3.) Leftmost zeros appearing in front of nonzero digits are
not significant.
examples: these have only 2:
0.0071 meter
0.42 meter
0. 0000099 meter
© Copyright Pearson Prentice Hall
Measurements and Their Uncertainty
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Slide 19 of 48
Significant Figures in Measurements3.1
4.) Zeros at the end of a number and to the right of a
decimal point are always significant.
examples: these have 4 in them:
43.00 meters
1.010 meters
9.000 meters
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Measurements and Their Uncertainty
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Slide 20 of 48
Significant Figures in Measurements3.1
5.) Zeros at the rightmost end of a measurement that lie
to the left of an understood decimal point are not
significant if they show as placeholders.
examples:
300 meters = 1
7000 meters = 1
27210 meters = 4
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Measurements and Their Uncertainty
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Slide 21 of 48
Significant Figures in Measurements3.1
6.) All digits in a scientific notation is significant.
ex. 1.28 x 10 3 = 3
5. 1 x 10 4 = 2
6.000245 x 10 9 = 7
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Slide 22 of 48
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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Slide 26 of 48
Practice Problems
Problem Solving 3.2 Solve Problem 2 with the help of an interactive guided tutorial.
for Conceptual Problem 3.1
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Measurements and Their Uncertainty
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Slide 27 of 48
3.1 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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Slide 32 of 48
Practice Problems
Problem Solving 3.3 Solve Problem 3 with the help of an interactive guided tutorial.
for Sample Problem 3.1
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Measurements and Their Uncertainty
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Slide 33 of 48
3.1 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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Slide 38 of 48
Practice Problems for Sample Problem 3.2
Problem Solving 3.6 Solve Problem 6 with the help of an interactive guided tutorial.
© Copyright Pearson Prentice Hall
Measurements and Their Uncertainty
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Slide 39 of 48
3.1 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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Slide 44 of 48
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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Slide 45 of 48
Section Quiz
-or-Continue to: Launch:
Assess students’ understanding of the concepts in Section 3.1.
Section Assessment
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Slide 46 of 48
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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Slide 47 of 48
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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Slide 48 of 48
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
3.1 Section Quiz
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