© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 1 of Using and Expressing Measurements A ___________________ is a quantity that has both a __________ and a __________. 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 2 of Using and Expressing Measurements In ____________ _______________, a given number is written as the __________ of two numbers: a _________________ and 10 raised to a _____________. The number of stars in a galaxy is an example of an estimate that should be expressed in scientific notation.

© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 3 of Accuracy, Precision, and Error Accuracy and Precision ________________ is a measure of ______ _______________ a measurement comes to the __________ or ________ value of whatever is measured. _______________ is a measure of how close a series of measurements are to _________ ______________________

© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 4 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 5 of Accuracy, Precision, and Error

© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 6 of Accuracy, Precision, and Error Determining Error The ____________ value is the correct value based on reliable references. The ______________ value is the value measured in the lab. The difference between the experimental value and the accepted value is called the _____________.

© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 7 of Accuracy, Precision, and Error The ___________ _________________ is the absolute value of the error divided by the accepted value, multiplied by 100%.

© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 8 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 ___________ ___________________ 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 9 of 48 Significant Figures in Measurements ___________________ must always be reported to the correct number of ___________ ______________ 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 10 of 48 1._______-________ ___________ are assumed to be significant. 2._______ ______ are always significant. 3._______ _________ are never significant. 4._________ _____________ count if there is a decimal point present. 5.Counting number and conversion factors are considered significant to an infinite degree.

© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 11 of 48 Significant Figures in Measurements 3.1

© Copyright Pearson Prentice Hall Slide 12 of 48

© Copyright Pearson Prentice Hall Slide 13 of 48 Practice Problems Problem Solving 3.2 Solve Problem 2 with the help of an interactive guided tutorial. for Conceptual Problem 3.1

Slide 14 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. The calculated value must be ____________ to make it consistent with the measurements from which it was calculated. 3.1

© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 15 of Significant Figures in Calculations Rounding To round a number, you must first decide how many _________ ___________ your answer should have. The answer depends on the given measurements and on the mathematical ______________ used to arrive at the answer.

© Copyright Pearson Prentice Hall SAMPLE PROBLEM Slide 16 of

© Copyright Pearson Prentice Hall Slide 17 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 18 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 19 of

© Copyright Pearson Prentice Hall Slide 20 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 21 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. The position of the decimal point has nothing to do with the rounding process when multiplying and dividing measurements.

© Copyright Pearson Prentice Hall SAMPLE PROBLEM Slide 22 of

© Copyright Pearson Prentice Hall Slide 23 of 48 Practice Problems for Sample Problem 3.3 Problem Solving 3.8 Solve Problem 8 with the help of an interactive guided tutorial.