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? Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved.

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. Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved.

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.) Slide of 48 3 End Show © Copyright Pearson Prentice Hall

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? Slide of 48 4 End Show © Copyright Pearson Prentice Hall

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. Slide of 48 5 End Show © Copyright Pearson Prentice Hall

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. Slide of 48 6 End Show © Copyright Pearson Prentice Hall

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. Slide of 48 7 End Show © Copyright Pearson Prentice Hall

Accuracy and Precision Section 3 Using Scientific Measurements Chapter 2 Accuracy and Precision Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved.

Accuracy and Precision Visual Concepts Chapter 2 Accuracy and Precision Click below to watch the Visual Concept. http://my.hrw.com/sh/hc6_003036809x/student/ch02/sec03/vc00/hc602_03_v00fs.htm Visual Concept Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved.

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? Slide of 48 10 End Show © Copyright Pearson Prentice Hall

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. Slide of 48 11 End Show © Copyright Pearson Prentice Hall

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. Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved.

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 Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved.

PERCENT ERROR PROBLEM ACTIVITY CLICK HERE FOR PERCENT ERROR PROBLEM ACTIVITY Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved.

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? Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved.

Accuracy and Precision, continued Section 3 Using Scientific Measurements Chapter 2 Accuracy and Precision, continued Sample Problem C Solution Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved.

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 Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved.

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. Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved.

Section 3 Using Scientific Measurements Chapter 2 Sig. figs. in a measurement include the known digits plus a final estimated digit Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved.

Chapter 2 Significant Figures Visual Concepts Chapter 2 Significant Figures Click below to watch the Visual Concept. http://my.hrw.com/sh/hc6_003036809x/student/ch02/sec03/vc02/hc602_03_v02fs.htm Visual Concept Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved.

Significant Figures, continued Section 3 Using Scientific Measurements Chapter 2 Significant Figures, continued Determining the Number of Significant Figures Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved.

Rules for Determining Significant Zeros Visual Concepts Chapter 2 Rules for Determining Significant Zeros Click below to watch the Visual Concept. http://my.hrw.com/sh/hc6_003036809x/student/ch02/sec03/vc03/hc602_03_v03fs.htm Visual Concept Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved.

Counting Sig Fig Examples C. Significant Figures Counting Sig Fig Examples 1. 23.50 1. 23.50 4 sig figs 2. 402 2. 402 3 sig figs 3. 5,280 3. 5,280 3 sig figs 4. 0.080 4. 0.080 2 sig figs C. Johannesson

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. 28.6 g b. 3440. cm c. 910 m d. 0.046 04 L e. 0.006 700 0 kg Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved.

Significant Figures, continued Section 3 Using Scientific Measurements Chapter 2 Significant Figures, continued Sample Problem D Solution a. 28.6 g There are no zeros, so all three digits are significant. b. 3440. 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. Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved.

Significant Figures, continued Section 3 Using Scientific Measurements Chapter 2 Significant Figures, continued Sample Problem D Solution, continued d. 0.046 04 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. 0.006 700 0 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. Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved.

SIG. FIG. PRACTICE QUESTIONS Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved.

SIG. FIG. ANSWERS - CHECK WORK Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved.

Significant Figures, continued Section 3 Using Scientific Measurements Chapter 2 Significant Figures, continued Rounding Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved.

Rules for Rounding Numbers Visual Concepts Chapter 2 Rules for Rounding Numbers Click below to watch the Visual Concept. http://my.hrw.com/sh/hc6_003036809x/student/ch02/sec03/vc04/hc602_03_v04fs.htm Visual Concept Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved.

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) = 324.103g 4 SF 3 SF 3 SF 324 g C. Johannesson

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 + 4.1 mL 7.85 mL 3.75 mL + 4.1 mL 7.85 mL 224 g + 130 g 354 g 224 g + 130 g 354 g → 7.8 mL → 350 g C. Johannesson

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

C. Significant Figures Practice Problems f). (15.30 g) ÷ (6.4 mL) g). 18.9 g - 0.84 g → 18.1 g 18.06 g C. Johannesson

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

D. Scientific Notation Practice Problems h. 2,400,000 μg 2.4 × 106 μg i. 0.00256 kg j. 7 × 10-5 km k. 6.2 × 104 mm 2.4 × 106 μg 2.56 × 10-3 kg 0.00007 km 62,000 mm C. Johannesson

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 = 671.6049383 = 670 g/mol = 6.7 × 102 g/mol C. Johannesson

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) Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved.

E. Proportions Direct Proportion Inverse Proportion y x y x C. Johannesson

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 Slide of 48 End Show © Copyright Pearson Prentice Hall

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? 0.00456 × 10–8 = 4.56 × 10–11 454 × 10–8 = 4.54 × 10–6 842.6 × 104 = 8.426 × 106 0.00452 × 106 = 4.52 × 109 Slide of 27 End Show © Copyright Pearson Prentice Hall

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 Slide of 27 End Show © Copyright Pearson Prentice Hall

2.3 Section Quiz 3. A student reports the volume of a liquid as 0.0130 L. How many significant figures are in this measurement? 2 3 4 5 Slide of 27 End Show © Copyright Pearson Prentice Hall

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. Slide of 25 End Show © Copyright Pearson Prentice Hall

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) Slide of 27 End Show © Copyright Pearson Prentice Hall

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) Slide of 27 End Show © Copyright Pearson Prentice Hall

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 www.scilinks.org 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 Slide of 27 End Show © Copyright Pearson Prentice Hall

End of Chapter 2.3 Show Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved.