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1 Chapter 2 Analyzing Data

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2 Section 2.3 Uncertainty in Data

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3 Objectives Define and compare accuracy and precision. Describe the accuracy of experimental data using error and percent error. Apply rules for significant figures to express uncertainty in measured and calculated values.

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4 Review Vocabulary experiment: a set of controlled observations that test a hypothesis New Vocabulary accuracypercent error precisionsignificant figures error

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5 Measurements contain uncertainties that affect how a result is presented.

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6 Accuracy and Precision Accuracy refers to how close a measured value is to an accepted value. Precision refers to how close a series of measurements are to one another.

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7 Accuracy and Precision Error is defined as the difference between an experimental value and an accepted value. Table 2.3 Student Density and Error Data (Unknown was sucrose; density = 1.59 g/cm 3 ) Student AStudent BStudent C Density (g/cm 3 ) Error (g/cm 3 ) Density (g/cm 3 ) Error (g/cm 3 ) Density (g/cm 3 ) Error (g/cm 3 ) Trial Trial Trial Average

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8 Accuracy and Precision The error equation is error = experimental value – accepted value ( = 1.54 g/cm 3 – 1.59 g/cm 3 = g/cm 3 ) Table 2.3 Student Density and Error Data (Unknown was sucrose; density = 1.59 g/cm 3 ) Student AStudent BStudent C Density (g/cm 3 ) Error (g/cm 3 ) Density (g/cm 3 ) Error (g/cm 3 ) Density (g/cm 3 ) Error (g/cm 3 ) Trial Trial Trial Average

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9 Accuracy and Precision The error equation is error = experimental value – accepted value ( = 1.54 g/cm 3 – 1.59 g/cm 3 = g/cm 3 ) Percent error expresses error as a percentage of the accepted value: Percent error = |error| accepted value x 100% = 0.05 g/cm 3 ÷ 1.59 g/cm 3 x 100% = 3.14 %

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10 Significant Figures Often, precision is limited by the tools available. Significant figures include all known digits plus one estimated (uncertain) digit. 11 cm is a known digit 0.6 cm is a known digit 0.05 cm is an estimated digit

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11 Significant Figures Rules for significant figures: Rule 1: Nonzero numbers are always significant. Rule 2: Zeros between nonzero numbers are always significant. Rule 3: All final zeros to the right of the decimal are significant. Rule 4: Placeholder zeros are not significant. To remove placeholder zeros, rewrite the number in scientific notation. Rule 5: Counting numbers and defined constants have an infinite number of significant figures.

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12 Rounding Numbers Calculators are not aware of significant figures. Answers should not have more significant figures than the original data with the fewest figures, and should be rounded.

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13 Rounding Numbers Rules for rounding: Rule 1: If the digit to the right of the last significant figure is less than 5, do not change the last significant figure. Rule 2: If the digit to the right of the last significant figure is 5 or greater, round up the last significant figure

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14 Rounding Numbers Addition and subtraction Round numbers so all numbers have the same number of digits to the right of the decimal = = =

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15 Rounding Numbers Multiplication and division Round the answer to the same number of significant figures as the original measurement with the fewest significant figures * =

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16 Assessment Determine the number of significant figures in the following: 8 200, 723.0, and 0.01 A. 4, 4, and 3 B. 4, 3, and 3 C. 2, 3, and 1 D. 2, 4, and 1

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17 Assessment Determine the number of significant figures in the following: 8 200, 723.0, and 0.01 A. 4, 4, and 3 B. 4, 3, and 3 C. 2, 3, and 1 D. 2, 4, and 1

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18 Assessment A substance has an accepted density of 2.00 g/L. You measured the density as 1.80 g/L. What is your percent error? A g/L B g/L C g/L D g/L

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19 Assessment A substance has an accepted density of 2.00 g/L. You measured the density as 1.80 g/L. What is your percent error? A g/L B g/L C g/L D g/L

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