Accuracy, Precision, and Significant Figures PDF

3.1 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....

3.1 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. Slide 1 of 48 © Copyright Pearson Prentice Hall  3.1 Measurements and Their > Using and Expressing Measurements Uncertainty Using and Expressing Measurements How do measurements relate to science? Slide 2 of 48 © Copyright Pearson Prentice Hall 3.1 Measurements and Their > Using and Expressing Measurements Uncertainty 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. Slide 3 of 48 © Copyright Pearson Prentice Hall 3.1 Measurements and Their > Using and Expressing Measurements Uncertainty In scientific notation, a given number is written as the product of two numbers: 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. Slide 4 of 48 © Copyright Pearson Prentice Hall  3.1 Measurements and Their > Accuracy, Precision, and Error Uncertainty Accuracy, Precision, and Error How do you evaluate accuracy and precision? Slide 5 of 48 © Copyright Pearson Prentice Hall  3.1 Measurements and Their > Accuracy, Precision, and Error Uncertainty 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 6 of 48 © Copyright Pearson Prentice Hall 3.1 Measurements and Their > Accuracy, Precision, and Error Uncertainty 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 7 of 48 © Copyright Pearson Prentice Hall 3.1 Measurements and Their > Accuracy, Precision, and Error Uncertainty Slide 8 of 48 © Copyright Pearson Prentice Hall  3.1 Measurements and Their > Accuracy, Precision, and Error Uncertainty 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 9 of 48 © Copyright Pearson Prentice Hall 3.1 Measurements and Their > Accuracy, Precision, and Error Uncertainty The percent error is the absolute value of the error divided by the accepted value, multiplied by 100%. Slide 10 of 48 © Copyright Pearson Prentice Hall 3.1 Measurements and Their > Accuracy, Precision, and Error Uncertainty Slide 11 of 48 © Copyright Pearson Prentice Hall 3.1 Measurements and Their > Accuracy, Precision, and Error Uncertainty 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. Slide 12 of 48 © Copyright Pearson Prentice Hall  3.1 Measurements and Their > Significant Figures in Measurements Uncertainty Significant Figures in Measurements Why must measurements be reported to the correct number of significant figures? Slide 13 of 48 © Copyright Pearson Prentice Hall 3.1 Measurements and Their > Significant Figures in Measurements Uncertainty 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. Slide 14 of 48 © Copyright Pearson Prentice Hall 3.1 Measurements and Their > Significant Figures in Measurements Uncertainty 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. Slide 15 of 48 © Copyright Pearson Prentice Hall Measurements and Their > Uncertainty Rules for Significant Figures: 1. Every nonzero digit in a measurement is assumed to be significant. For example, the measurements 24.7 meters, 0.743 meters and 714 meters each have three significant figures Slide 16 of 48 © Copyright Pearson Prentice Hall Measurements and Their > Uncertainty Rules for Significant Figures: 2. Zeros appearing between nonzero digits are significant. For example, the measurements 7003 meters, 40.79 meters, and 1.503 meters each have four significant figures. Slide 17 of 48 © Copyright Pearson Prentice Hall Measurements and Their > Uncertainty Rules for Significant Figures: 3. Leftmost zeros appearing in front of nonzero digits are not significant. They act as place holders. For example the measurements 0.0071meters, 0.42 meters, and 0.0000099 meters each have two significant figures. Slide 18 of 48 © Copyright Pearson Prentice Hall Measurements and Their > Uncertainty Rules for Significant Figures: 4. Zeros at the end of a number and to the right of a decimal point are always significant. For example, the measurements 43.00 meters, 1.010 meters, and 9.000 meters each have four significant figure. Slide 19 of 48 © Copyright Pearson Prentice Hall 3.1 Measurements and Their > Significant Figures in Measurements Uncertainty Insert Insert Illustration Illustration of aofsheet a sheetof paper of paper listing listing the the six rules six rules for determining for determining whetherwhether a digit ina adigit measured in a measured value isvalue significant. is Redosignificant. the illustration Redo the as process illustration art. Each as process rule should art. Eachbe rule a separate shouldimage. be a separate image. Slide 20 of 48 © Copyright Pearson Prentice Hall Measurements and Their > Uncertainty Slide 21 of 48 © Copyright Pearson Prentice Hall  Measurements and Their > Significant Figures in Measurements Uncertainty Animation 2 See how the precision of a calculated result depends on the sensitivity of the measuring instruments. Slide 22 of 48 © Copyright Pearson Prentice Hall 3.1 Measurements and Their > Significant Figures in Measurements Uncertainty Slide 23 of 48 © Copyright Pearson Prentice Hall  Slide 24 of 48 © Copyright Pearson Prentice Hall  Slide 25 of 48 © Copyright Pearson Prentice Hall  Slide 26 of 48 © Copyright Pearson Prentice Hall  3.1 Measurements and Their > Significant Figures in Calculations Uncertainty Significant Figures in Calculations How does the precision of a calculated answer compare to the precision of the measurements used to obtain it? Slide 27 of 48 © Copyright Pearson Prentice Hall 3.1 Measurements and Their > Significant Figures in Calculations Uncertainty 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. Slide 28 of 48 © Copyright Pearson Prentice Hall  3.1 Measurements and Their > Significant Figures in Calculations Uncertainty 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. Slide 29 of 48 © Copyright Pearson Prentice Hall SAMPLE PROBLEM 3.1 Slide 30 of 48 © Copyright Pearson Prentice Hall SAMPLE PROBLEM 3.1 Slide 31 of 48 © Copyright Pearson Prentice Hall SAMPLE PROBLEM 3.1 Slide 32 of 48 © Copyright Pearson Prentice Hall SAMPLE PROBLEM 3.1 Slide 33 of 48 © Copyright Pearson Prentice Hall Practice Problems for Sample Problem 3.1 Problem Solving 3.3 Solve Problem 3 with the help of an interactive guided tutorial. Slide 34 of 48 © Copyright Pearson Prentice Hall  3.1 Measurements and Their > Significant Figures in Calculations Uncertainty 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. Slide 35 of 48 © Copyright Pearson Prentice Hall SAMPLE PROBLEM 3.2 Slide 36 of 48 © Copyright Pearson Prentice Hall SAMPLE PROBLEM 3.2 Slide 37 of 48 © Copyright Pearson Prentice Hall SAMPLE PROBLEM 3.2 Slide 38 of 48 © Copyright Pearson Prentice Hall SAMPLE PROBLEM 3.2 Slide 39 of 48 © Copyright Pearson Prentice Hall Practice Problems for Sample Problem 3.2 Problem Solving 3.6 Solve Problem 6 with the help of an interactive guided tutorial. Slide 40 of 48 © Copyright Pearson Prentice Hall  3.1 Measurements and Their > Significant Figures in Calculations Uncertainty 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. Slide 41 of 48 © Copyright Pearson Prentice Hall SAMPLE PROBLEM 3.3 Slide 42 of 48 © Copyright Pearson Prentice Hall SAMPLE PROBLEM 3.3 Slide 43 of 48 © Copyright Pearson Prentice Hall SAMPLE PROBLEM 3.3 Slide 44 of 48 © Copyright Pearson Prentice Hall SAMPLE PROBLEM 3.3 Slide 45 of 48 © Copyright Pearson Prentice Hall Practice Problems for Sample Problem 3.3 Problem Solving 3.8 Solve Problem 8 with the help of an interactive guided tutorial. Slide 46 of 48 © Copyright Pearson Prentice Hall Section Assessment Assess students’ understanding of the concepts in Section 3.1. Continue to: Launch: -or- Section Quiz Slide 47 of 48 © Copyright Pearson Prentice Hall 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 Slide 48 of 48 © Copyright Pearson Prentice Hall 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 Slide 49 of 48 © Copyright Pearson Prentice Hall 3.1 Section Quiz 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 Slide 50 of 48 © Copyright Pearson Prentice Hall END OF SHOW