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© Copyright Pearson Prentice Hall
Slide 1 of 48
3.1 Measurements and Their Uncertainty
On January 4, 2004, the Mars Exploration Rover Spirit landed on Mars. Each day of its mission, Spirit recorded measurements for analysis. In the chemistry laboratory, you must strive for accuracy and precision in your measurements.
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Measurements and Their Uncertainty
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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.
Measurements are fundamental to the experimental sciences. For that reason, it is important to be able to make measurements and to decide whether a measurement is correct.
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Measurements and Their Uncertainty
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Slide 4 of 48
3.1 Using and Expressing Measurements
Scientific Notation:
A given number is written as a product of its significant figures times 10n.
602,000,000,000,000,000,000,000 = 6.02x1023
Try these:
.00602, 72500, 100000
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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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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.
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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.
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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
Accuracy, Precision, and Error3.1
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Measurements and Their Uncertainty
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Slide 11 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.
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Measurements and Their Uncertainty
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Slide 12 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 13 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 14 of 48
Significant Figures in Measurements
Measurements must always be reported to the correct number of significant figures because 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 15 of 48
Significant Figures in Measurements
What’s significant?
•Every non-zero digit in a number
•Zeros appearing between non-zero digits.
•Left most zeros (ex. 0.000059) are not sigificant.
• How many sig figs do we have?
3.1
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Measurements and Their Uncertainty
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Slide 16 of 48
Significant Figures in Measurements
What’s significant?
•Zeros at the end of the number and to the right of the decimal are significant.
• Ex. (43.00, 1.010) How many sig figs?
•Zeros to the right most end of the measurement and to the left of the decimal (ex. 435,000,000) are NOT significant unless they are a known measurement.
3.1
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Measurements and Their Uncertainty
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Slide 17 of 48
Significant Figures in Measurements3.1
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Slide 18 of 48
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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 20 of 48
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?
3.1
Slide 21 of 48
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Measurements and Their Uncertainty
> Significant Figures in Calculations
In general, a calculated answer cannot be more precise than the least precise measurement from which it was calculated.
3.1
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Measurements and Their Uncertainty
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Slide 22 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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SAMPLE PROBLEM
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3.1
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SAMPLE PROBLEM
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3.1
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Slide 25 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 26 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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SAMPLE PROBLEM
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3.2
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SAMPLE PROBLEM
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3.2
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SAMPLE PROBLEM
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3.2
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Slide 30 of 48
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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Measurements and Their Uncertainty
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Slide 31 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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SAMPLE PROBLEM
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3.3
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SAMPLE PROBLEM
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3.3
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Slide 34 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 35 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 36 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 37 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