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Chemistry 3.1 Uncertainty in Measurements

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I. Accuracy, Precision, & Error A. Accuracy – how close a measurement comes to the “true value”. 1. Ex: Throwing Darts true value = bull's-eye

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B. Precision – how close a series of measurements are together. 1. Ex: Throwing Darts

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C. Pg. 64 Explanation Poor Accuracy Good Precision Good Accuracy Good Precision Poor Accuracy Poor Precision

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D. Error – the difference between the accepted value and the experimental value. 1. Formula – 2. Error = ex. value – accepted value | error | accepted value

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E. Examples 1. In class you determine the melting point of salt is 755 deg C. The actual value is 805 deg C. What is your percent error? [|755 - 805| / 805] x 100 = 6.2% error

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II. Significant Figures A. Def – all digits known plus one estimated one. 1. Measurements must be recorded with significant figures.

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2. Rules (pg.66) -All other numbers are significant -zeros may or may not be significant -leading zeros are not significant 0.021 (sig fig) -captive zeros are significant 0.02033 (sig figs) -trailing zeros following the decimal point are significant 0.02030? (sig figs) 200 ? (sig figs) 200.0? (sig figs) 4 1 4

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3. Rounding with Sig Figs -Express the following #’s to 3 sig figs 421798.076 = 422,000 0.00099985 =.00100 1 = 1.00 8222 = 8,220 0.42 =.420

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4. Scientific Notation + Sig figs A. All #’s in scientific notation are counted as significant figures. B. Ex: 3.0200 x 10 3 = sig figs 2.77 x 10 6 = sig figs 5 3

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5. Adding and subtracted A. The answer must not contain any sig figs beyond the place value common to all #’s B. Ex: 4.8 + 2.015 6.8 (not 6.815)

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6. Multiplication and Division A. The answer must not contain more sig figs than the least # of sig figs. B. Ex:3.1 x 4.01 12 (not 12.431)

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In Class Problems 1. How many sig figs? -123 meters-30.0 meters -40,506 kg-6.455 x 10 3 kg 2. 3.45 + 9.001 and 4.22 - 9.0 3. 3.4 x 5.345 and 10.7 / 12.75 4. 6.33 x 10 3 + 5.1 x 10 4

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