1. Chapter 2 Lesson Starter
Section 3 Using Scientific Measurements
Chapter 2
Lesson Starter
Look at the specifications for electronic balances. How do the instruments vary in precision?
Discuss using a beaker to measure volume versus using a graduated cylinder. Which is more precise?
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2. Chapter 2 Objectives **Distinguish between accuracy and precision.
Section 3 Using Scientific Measurements
Chapter 2
Objectives
**Distinguish between accuracy and precision.
**Determine the number of significant figures in measurements.
Perform mathematical operations involving significant figures.
Convert measurements into scientific notation.
Distinguish between inversely and directly proportional relationships.
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3. Measurements and Their Uncertainty
2.3
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. (In August 2012, a new rover landed on Mars to collect data.)
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4. Accuracy, Precision, and Error
2.3
Measurements and Their Uncertainty
>
Accuracy, Precision, and Error
Accuracy, Precision, and Error
How do you evaluate accuracy and precision?
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5. Accuracy, Precision, and Error
2.3
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.
Precision is a measure of how close a series of measurements are to one another.
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6. Accuracy, Precision, and Error
2.3
Measurements and Their Uncertainty
>
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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7. Accuracy, Precision, and Error
2.3
Measurements and Their Uncertainty
>
Accuracy, Precision, and Error
The distribution of darts illustrates the difference between accuracy and precision. a) Good accuracy and good precision: The darts are close to the bull’s-eye and to one another. b) Poor accuracy and good precision: The darts are far from the bull’s-eye but close to one another. c) Poor accuracy and poor precision: The darts are far from the bull’s-eye and from one another.
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8. Accuracy and Precision
Section 3 Using Scientific Measurements
Chapter 2
Accuracy and Precision
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9. Accuracy and Precision
Visual Concepts
Chapter 2
Accuracy and Precision
Click below to watch the Visual Concept.
Visual Concept
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10. Accuracy, Precision, and Error
2.3
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.
The scale below has not been properly zeroed, so the reading obtained for the person’s weight is inaccurate. There is a difference between the person’s correct weight and the measured value. Calculating What is the percent error of a measured value of 114 lb if the person’s actual weight is 107 lb?
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11. Accuracy, Precision, and Error
2.3
Measurements and Their Uncertainty
>
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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12. Accuracy and Precision, continued
Section 3 Using Scientific Measurements
Chapter 2
Accuracy and Precision, continued
Percentage Error
Percentage error is calculated by subtracting the accepted value from the experimental value, dividing the difference by the accepted value, and then multiplying by 100.
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13. Chapter 2 Percentage Error Visual Concept
Section 3 Using Scientific Measurements
Chapter 2
Percentage Error
Visual Concept
Click below for Visual Concept
Click for Visual Concept on Percent Error
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14. PERCENT ERROR PROBLEM ACTIVITY
CLICK HERE FOR PERCENT ERROR PROBLEM ACTIVITY
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15. Accuracy and Precision, continued
Section 3 Using Scientific Measurements
Chapter 2
Accuracy and Precision, continued
Problem Example - RECORD in notes before checking.
A student measures the mass and volume of a substance and calculates its density as 1.40 g/mL. The correct, or accepted, value of the density is 1.30 g/mL. What is the percentage error of the student’s measurement?
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16. Accuracy and Precision, continued
Section 3 Using Scientific Measurements
Chapter 2
Accuracy and Precision, continued
Sample Problem C Solution
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17. Accuracy and Precision, continued
Section 3 Using Scientific Measurements
Chapter 2
Accuracy and Precision, continued
Error in Measurement
Some error or uncertainty always exists in any measurement.
skill of the measurer
conditions of measurement
measuring instruments
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18. Chapter 2 Significant Figures
Section 3 Using Scientific Measurements
Chapter 2
Significant Figures
Significant figures in a measurement consist of all the digits known with certainty plus one final digit, which is somewhat uncertain or is estimated.
The term significant does not mean certain.
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19. Section 3 Using Scientific Measurements
Chapter 2
Sig. figs. in a measurement include the known digits plus a final estimated digit
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20. Chapter 2 Significant Figures
Visual Concepts
Chapter 2
Significant Figures
Click below to watch the Visual Concept.
Visual Concept
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21. Significant Figures, continued
Section 3 Using Scientific Measurements
Chapter 2
Significant Figures, continued
Determining the Number of Significant Figures
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22. Rules for Determining Significant Zeros
Visual Concepts
Chapter 2
Rules for Determining Significant Zeros
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Visual Concept
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23. Counting Sig Fig Examples
C. Significant Figures
Counting Sig Fig Examples
4 sig figs
3 sig figs
3. 5,280
3. 5,280
3 sig figs
2 sig figs
C. Johannesson

24. Significant Figures, continued
Section 3 Using Scientific Measurements
Chapter 2
Significant Figures, continued
Sample Problem D
How many significant figures are in each of the following measurements?
a g
b cm
c. 910 m
d L
e kg
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25. Significant Figures, continued
Section 3 Using Scientific Measurements
Chapter 2
Significant Figures, continued
Sample Problem D Solution
a g
There are no zeros, so all three digits are significant.
b cm
By rule 4, the zero is significant because it is immediately followed by a decimal point; there are 4 significant figures.
c. 910 m
By rule 4, the zero is not significant; there are 2 significant figures.
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26. Significant Figures, continued
Section 3 Using Scientific Measurements
Chapter 2
Significant Figures, continued
Sample Problem D Solution, continued
d L
By rule 2, the first two zeros are not significant; by rule 1, the third zero is significant; there are 4 significant figures.
e kg
By rule 2, the first three zeros are not significant; by rule 3, the last three zeros are significant; there are 5 significant figures.
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27. SIG. FIG. PRACTICE QUESTIONS
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28. SIG. FIG. ANSWERS - CHECK WORK
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29. Significant Figures, continued
Section 3 Using Scientific Measurements
Chapter 2
Significant Figures, continued
Rounding
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30. Rules for Rounding Numbers
Visual Concepts
Chapter 2
Rules for Rounding Numbers
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Visual Concept
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31. C. Significant Figures (13.91g/cm3)(23.3cm3) = 324.103g 324 g
Calculating with Sig Figs
Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer.
(13.91g/cm3)(23.3cm3) = g
4 SF
3 SF
3 SF
324 g
C. Johannesson

32. C. Significant Figures 3.75 mL + 4.1 mL 7.85 mL 3.75 mL + 4.1 mL
Calculating with Sig Figs (con’t)
Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer.
3.75 mL mL
7.85 mL
3.75 mL mL
7.85 mL
224 g
+ 130 g
354 g
224 g
+ 130 g
354 g
→ 7.8 mL
→ 350 g
C. Johannesson

33. C. Significant Figures Calculating with Sig Figs (con’t)
Exact Numbers do not limit the # of sig figs in the answer.
Counting numbers: 12 students
Exact conversions: 1 m = 100 cm
“1” in any conversion: 1 in = 2.54 cm
C. Johannesson

34. C. Significant Figures Practice Problems f). (15.30 g) ÷ (6.4 mL)
g) g g
→ 18.1 g
18.06 g
C. Johannesson

35. D. Scientific Notation 65,000 kg → 6.5 × 104 kg
Converting into Sci. Notation:
Move decimal until there’s 1 digit to its left. Places moved = exponent.
Large # (>1) ⇒ positive exponent Small # (<1) ⇒ negative exponent
Only include sig figs.
C. Johannesson

36. D. Scientific Notation Practice Problems h. 2,400,000 μg 2.4 × 106 μg
i kg
j. 7 × km
k. 6.2 × 104 mm
2.4 × 106 μg
2.56 × 10-3 kg km
62,000 mm
C. Johannesson

37. D. Scientific Notation Calculating with Sci. Notation
(5.44 × 107 g) ÷ (8.1 × 104 mol) =
Type on your calculator:
EXP EE
EXP EE
ENTER
EXE
5.44 7 ÷
8.1 4 =
= 670 g/mol
= 6.7 × 102 g/mol
C. Johannesson

38. Stop here and play BINGO GAME ACTIVITY
HW: Study Guide Questions due on Friday.
Get out a sheet of paper and make a 5 x 5 grid. (5 rows and 5 columns)
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39. E. Proportions Direct Proportion Inverse Proportion y x y x
C. Johannesson

40. Assess students’ understanding of the concepts in Section 2.3.
Section Assessment
Assess students’ understanding of the concepts in Section
2.3.
Continue to: Launch:
-or-
Section Quiz
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41. 2.3 Check up Section Quiz
1. In which of the following expressions is the number on the left NOT equal to the number on the right?
× 10–8 = 4.56 × 10–11
454 × 10–8 = 4.54 × 10–6
842.6 × 104 = × 106
× 106 = 4.52 × 109
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42. 2. Which set of measurements of a 2.00-g standard is the most precise?
2.3 Section Quiz
2. Which set of measurements of a 2.00-g standard is the most precise?
2.00 g, 2.01 g, 1.98 g
2.10 g, 2.00 g, 2.20 g
2.02 g, 2.03 g, 2.04 g
1.50 g, 2.00 g, 2.50 g
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43. 2.3 Section Quiz
3. A student reports the volume of a liquid as L. How many significant figures are in this measurement? 2 3 4 5
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44. Online Self-Check Quiz
Complete the online 2.3 Quiz and record answers. Ask if you have any questions about your answers.
Click here for Section 2.3 QUIZ(10 questions)
Some of these are challenging. Ask if you miss and need help understanding. It is imperative you get help when something doesn’t make sense to be successful.
You must be in the “Play mode” for the slideshow for hyperlink to work.
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45. VIDEOS FOR ADDITIONAL INSTRUCTION
Additional Videos for Section 2.3 Using Scientific Measurements (4 videoclips)
Direct Variation (1:44)
Inverse Variation (2:12)
Significant Figures (6:04)
Scientific Notation (2:26)
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46. VIDEOS FOR ADDITIONAL INSTRUCTION
Additional Videos for Section 2.3 Using Scientific Measurements (4 videoclips)
Direct Variation (1:44)
Inverse Variation (2:12)
Significant Figures (6:04)
Scientific Notation (2:26)
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47. SCI LINKS FOR CHAPTER Additional Student SCI LINKS for CHAPTER 2
The NSTA-sponsored SciLinks Web site contains links to accurate and up-to-date science
information on the Internet. Just click on the button below to go to the SciLinks site at
and log in. Then, type in the SciLinks code for the topic you want to
research. The following is a list of the SciLinks codes for this chapter.
Chapter 2: Measurements and Calculations
Topic: Scientific Methods
SciLinks code: HC61359
Topic: SI Units
SciLinks code: HC61390
Topic: Significant Figures
SciLinks code: HC61392
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48. End of Chapter 2.3 Show Chapter menu Resources
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