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Unit 1- Units and Measurement Chemistry

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Scientific Notation, Measurement, Accuracy, Precision, Error

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Scientific Notation M x 10 n M is the coefficient 1<M<10 10 is the base n is the exponent or power of 10 n is positive if number is greater 1 n is negative if number is less 1

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Scientific Notation Write the following in scientific notation: 5450000 = 0.0002570 =

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Limits of Measurement Accuracy and Precision Uncertainty Exact Numbers vs. Inexact

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Accuracy - a measure of how close a measurement is to the true value of the quantity being measured.

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Example: Accuracy Who is more accurate when measuring a book that has a true length of 17.0cm? Susan: 17.0cm, 16.0cm, 18.0cm, 15.0cm Amy: 15.5cm, 15.0cm, 15.2cm, 15.3cm

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Precision – a measure of how close a series of measurements are to one another. A measure of how exact a measurement is.

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Example: Precision Who is more precise when measuring the same 17.0cm book? Susan: 17.0cm, 16.0cm, 18.0cm, 15.0cm Amy: 15.5cm, 15.0cm, 15.2cm, 15.3cm

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Example: Evaluate whether the following are precise, accurate or both.

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Error Error= experimental –accepted value

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Percent Error % Error= |experimental –accepted| x100 accepted value

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Significant Figures The significant figures in a measurement include all of the digits that are known, plus one last digit that is estimated. Uncertainty-

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Centimeters and Millimeters

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The last (farthest to the right) significant figure in a measured quantity always has some associated uncertainty. The minimum uncertainty is ± 1 in the last digit

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Graduated Cylinder - Meniscus

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Reading Scales to the Correct Significant Figures Uncertainty?

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Reading Scales to Correct Significant Figures

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Reading Scales to Correct Significant Figures Uncertainty?

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Rules for Counting Significant Figures All nonzero digits are significant. (42 has 2 sf’s.) Zeros in the middle of a number are significant. (4.803 cm has 4 sf’s.) Leading zeros are not significant; they are there to locate the decimal point. (0.00123 g has three sf’s.) Trailing zeros are significant if the number contains a decimal point. (55.220 K has five sf’s; 50.0 mg has three sf’s, 5.100 × 10-3 has four sf’s.) Trailing zeros are not significant if the number does not contain a decimal. (34,200 m has three sf’s.)

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How many sig figs? 100 kg 0.000303 mm 10302.00 cm92,900,000 km 0.001L6.02 x 10 23 atoms 10302 m0.0205 m 1.0302x10 4 ms2.05 x 10 -2 m 1010.010 g

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Sig Figs in Addition/Subtraction The result has the same number of decimal places as the number in the operation with the least decimal places. Ex: 2.33 cm +3.0 cm 5.3 cm

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Sig Figs in Multiplication/Division The answer has the same sig figs as the factor with the least sig figs. Ex: 3.22 cm x 2.0 cm 6.4 cm 2

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Measured Numbers vs. Exact Numbers Exact numbers are values that are known exactly (3 atoms = 3.00000…atoms) or that are true by definition: 12 inches = 1foot, 60 s = 1 min, 5280 feet = 1 mile, 100 cm = 1m, 2.54 cm = 1 inch, etc. All inexact or measured numbers will have some limit to how precisely they are known, and there is a limit to the number of significant digits contained in the number.

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