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Math in Chemistry During this unit, we will discuss: 1. Metric System 2. Exponential or Scientific Notation 3. Significant Digits 4. Dimensional Analysis

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Math in Chemistry Basic Definitions (pg. 55) Precision – the exactness of a measurement or the closeness of agreement of two or more measurements of the same quantity. Accuracy – how close a measurement is to the true value of the quantity measured

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Math in Chemistry

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Example: Suppose two sets of students were measuring 36.0 mL of water. The following is their data: Group 1Group 2 34.6 mL35.9 mL 34.2 mL36.0 mL 34.3mL35.9 mL Which group is precise? Which group is accurate?

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Math in Chemistry Percent Error - used to determine how close to the true values, or how accurate, an experimental value actually is. % Error = Experimental – Accepted Value x 100 Accepted Value

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Math in Chemistry Significant Figures (pgs. 56 – 59) Every measurement has some uncertainty to it, and that uncertainty should be indicated. Measurements are therefore reported as the number of digits that are known accurately plus the first uncertain digit (the doubtful digit).

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Math in Chemistry Rules for significant figures: 1. Nonzero digits are always significant. Ex: 45.6 m 2. Zeros between nonzero digits are significant Ex: 40.7 mL 3. Zeros in front of nonzero digits are not significant. Ex: 0.009587

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Math in Chemistry Significant Figures (continued) 4. Zeros both at the end of a number and to the right of a decimal point are significant. Ex: 85.00 g 5. The significance of numbers ending in zero that are not to the right of the decimal point can be unclear. They are significant only if the number contains a decimal point. Ex: 2000 m or 200.0 m

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Math in Chemistry Significant Figures (continued) 6. Exact numbers have not uncertainty and contain an infinite number of significant figures. These relationships are definitions, not measurements. Ex: There are exactly 1000 mL in one liter.

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Math in Chemistry Significant Figures (continued) 7. In exponential numbers, only the number portion of the number may be used when considering the number of significant figures. Ex: 1.03 x 10 20 3 x 10 30 (Exercise)

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Math in Chemistry Two quick rules can also be used: 1. If the number HAS a decimal point, start at the first non-zero number and keep counting. Ex: 0.090 =2 significant figures (bold)

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Math in Chemistry 2. If the number DOES NOT HAVE a decimal point, start counting at the first non-zero digit and STOP counting at the last non-zero digit. Ex: 20 400 3 sig figs (bold)

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Math in Chemistry Calculating with Significant Figures (pg 58) 1. Multiplication and Division - use the same number of significant digits as the term with the least number of S.D. Ex: 12.257 m 5 Sig Figs x 1.162 m 4 Sig Figs 14,2426234 Round off to 14.24 m 2

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Math in Chemistry Calculating with Significant Figures 2. Addition and Subtraction - use the number with the least amount of columns to determine the significant figures Ex:3.95 g 2.879 g 213.6 g 220.429 g Round to 220.4 g

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Math in Chemistry Calculating with Significant Figures 3. If a calculation has both addition/subtraction and multiplication/division, round after each operation.

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Math in Chemistry Scientific Notation (pg. 62) Very large or very small numbers appear frequently in chemistry. To make these numbers easier to work with and understand, scientific notation or exponential notation is used. Ex: 50,000,000 can be written as 5 x 10 7 The 7 tells us that the decimal point was moved to the left seven times.

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Math in Chemistry Rules for writing numbers is exponential form: 1. The exponent represents the number of places the decimal point has moved. 2. If the number is greater than one, the exponent must be positive. 3. If the number is less than one, the exponent is negative. 4. For this class, always shift the decimal point so that there is one significant figure to the left of the decimal point. 5. Always show all significant figures.

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Calculating with Exponents Multiplication without a calculator Multiply the significant portion Add the exponents Ex: x = (1.00 X 10 3 )(2.0 X 10 6 )

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Calculating with Exponents Division Divide the significant numbers Subtract the exponents Ex: 6.00 X 10 5 2.00 X 10 9

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Ch. 3.1 – Measurements and Their Uncertainty

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