Measurements and Their Uncertainty 3.1

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Measurements and Their Uncertainty 3.1

3.1

© Copyright Pearson Prentice Hall

Measurements and Their Uncertainty

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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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3.1 Using and Expressing Measurements

A measurement is a quantity that has both a number and a unit.



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3.1 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 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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To evaluate the precision of a measurement, you must compare the values of two or more repeated measurements.

Precision is a measure of how close a series of measurements are to one another.



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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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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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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 Error3.1



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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


Why must measurements be reported to the correct number of significant figures?

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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 Measurements3.1



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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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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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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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> 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 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.


SAMPLE PROBLEM

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SAMPLE PROBLEM

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SAMPLE PROBLEM

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Practice Problems


for Sample Problem 3.1



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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.


SAMPLE PROBLEM

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3.2


SAMPLE PROBLEM

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SAMPLE PROBLEM

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Practice Problems for Sample Problem 3.2




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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.


SAMPLE PROBLEM

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SAMPLE PROBLEM

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Practice Problems for Sample Problem 3.3



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Section Quiz

-or-Continue to: Launch:

Assess students’ understanding of the concepts in Section 3.1.

Section Assessment


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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

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Measurements and Their Uncertainty 3.1

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