© Copyright Pearson Prentice Hall Slide 1 of 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.

© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 2 of 48 Using and Expressing Measurements How do measurements relate to science? 3.1

© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 3 of 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.

© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 4 of Using and Expressing Measurements Scientific Notation: A given number is written as a product of its significant figures times 10 n. 602,000,000,000,000,000,000,000 = 6.02x10 23 Try these:.00602, 72500,

© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 5 of 48 Accuracy, Precision, and Error How do you evaluate accuracy and precision? 3.1

© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 6 of 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.

© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 7 of 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.

© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 8 of Accuracy, Precision, and Error

© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 9 of 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.

© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 10 of 48 Accuracy, Precision, and Error 3.1

© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 11 of 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.

© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 12 of 48 Significant Figures in Measurements Why must measurements be reported to the correct number of significant figures? 3.1

© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > 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

© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > 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

© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > 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 ) are not sigificant. How many sig figs do we have? 3.1

© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > 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

© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 17 of 48 Significant Figures in Measurements 3.1

© Copyright Pearson Prentice Hall Slide 18 of 48

© Copyright Pearson Prentice Hall Slide 19 of 48 Practice Problems Problem Solving 3.2 Solve Problem 2 with the help of an interactive guided tutorial. for Conceptual Problem 3.1

© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 20 of 48 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 © Copyright Pearson Prentice Hall 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

© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 22 of 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.

© Copyright Pearson Prentice Hall SAMPLE PROBLEM Slide 23 of

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© Copyright Pearson Prentice Hall 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

© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 26 of 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.

© Copyright Pearson Prentice Hall SAMPLE PROBLEM Slide 27 of

© Copyright Pearson Prentice Hall SAMPLE PROBLEM Slide 28 of

© Copyright Pearson Prentice Hall SAMPLE PROBLEM Slide 29 of

© Copyright Pearson Prentice Hall 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.

© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 31 of 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.

© Copyright Pearson Prentice Hall SAMPLE PROBLEM Slide 32 of

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© Copyright Pearson Prentice Hall 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.

© Copyright Pearson Prentice Hall Slide 35 of Section Quiz 1. In which of the following expressions is the number on the left NOT equal to the number on the right? a  10 –8 = 4.56  10 –11 b.454  10 –8 = 4.54  10 –6 c  10 4 =  10 6 d  10 6 = 4.52  10 9

© Copyright Pearson Prentice Hall Slide 36 of 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

© Copyright Pearson Prentice Hall Slide 37 of A student reports the volume of a liquid as L. How many significant figures are in this measurement? a.2 b.3 c.4 d Section Quiz