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Measurements and Their Uncertainty 3.1
3.1
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Measurements and Their Uncertainty
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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?
3.1
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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.
The calculated value must be rounded to make it consistent with the measurements from which it was calculated.
3.1
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Measurements and Their Uncertainty
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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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Practice Problems
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for Sample Problem 3.1
Write down your answers.
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Measurements and Their Uncertainty
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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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12.52 349.0 8.24 369.76
Final Answer 369.8 meters
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Practice Problems for Sample Problem 3.2
Write down your answers and round toThe correct number of SF’s..
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Measurements and Their Uncertainty
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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.
• The position of the decimal point has nothing to do with the rounding process when multiplying and dividing measurements.
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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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Practice Problems for Sample Problem 3.3
Write down your answer with the correctNumber of SF’s.
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Section Quiz
-or-Continue to: Launch:
Assess students’ understanding of the concepts in Section 3.1.
Section Assessment
Write down your answers.
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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. 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
END OF SHOW
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