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**Measurements and Their Uncertainty 3.1**

Section 3.1-1 3.1 Scientific Notation and % Error

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**Measurements and Their Uncertainty**

3.1 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.

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**Using and Expressing Measurements**

3.1 Using and Expressing Measurements Using and Expressing Measurements How do measurements relate to science?

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**Using and Expressing Measurements**

3.1 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.

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**Using and Expressing Measurements**

3.1 Using and Expressing Measurements 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. Expressing very large numbers, such as the estimated number of stars in a galaxy, is easier if scientific notation is used.

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**Accuracy, Precision, and Error**

3.1 Accuracy, Precision, and Error Accuracy, Precision, and Error How do you evaluate accuracy and precision?

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**Accuracy, Precision, and Error**

3.1 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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**Accuracy, Precision, and Error**

3.1 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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**Accuracy, Precision, and Error**

3.1 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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**Accuracy, Precision, and Error**

3.1 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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**Accuracy, Precision, and Error**

3.1 Accuracy, Precision, and Error The percent error is the absolute value of the error divided by the accepted value, multiplied by 100%. Expressing very large numbers, such as the estimated number of stars in a galaxy, is easier if scientific notation is used.

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**Accuracy, Precision, and Error**

3.1 Accuracy, Precision, and Error

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**Accuracy, Precision, and Error**

3.1 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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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? x 10–8 = 4.56 x 10–11 454 x 10–8 = 4.54 x 10–6 842.6 x 104 = x 106 x 106 = 4.52 x 109

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3.1 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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That’s All Folks ! ! !

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Chapter 2 Scientific Measurement. Chapter 2 Goals Calculate values from measurements using the correct number of significant figures. Calculate values.

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