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Scientific Notation Write 17,500 in scientific notation. 1.75 x 10 4 Write 0.0050 in scientific notation. 5.0 x 10 -3 5.0 x 10 -3 (3.0 x 10 5 )(5.0 x 10 -2 )= (3.0 x 5.0) x 10 5+(-2)

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Addition and subtraction: all numbers must be changed to the same exponent. Then add or subtract the numbers, attaching the common exponent. Addition and subtraction: all numbers must be changed to the same exponent. Then add or subtract the numbers, attaching the common exponent. ex.: 8.3 x 10 2 + 5.7 x 10 3 0.83 x 10 3 +5.7 x 10 3 +5.7 x 10 3 6.53 x 10 3 6.5 x 10 3

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Metric (SI) Base Units Length- meter Length- meter Mass- kilogram Mass- kilogram Volume- liter (displacement) Volume- liter (displacement) - cm 3 (L x W x H) - cm 3 (L x W x H) Temperature- Celsius C=5/9(F-32) Temperature- Celsius C=5/9(F-32) F = 9/5C +32 F = 9/5C +32 - Kelvin 0 ◦ C = 273 K - Kelvin 0 ◦ C = 273 K

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SI Prefixes SI Prefixes Giga10 9 Giga10 9 Mega10 6 Mega10 6 kilo10 3 basic unit deci10 -1 centi10 -2 milli10 -3 micro10 -6 nano10 -9 pico10 -12

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From DOE

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Significant Figures Indicate the uncertainty of a measurement

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The significant figures in a measurement are all the digits that are known with certainty, plus the first digit that is uncertain. The significant figures in a measurement are all the digits that are known with certainty, plus the first digit that is uncertain.

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Significant Figures All nonzero digits are significant 43.5 All nonzero digits are significant 43.5 Zeros are significant when... Zeros are significant when... between two nonzero digits 120.01 between two nonzero digits 120.01 to the right of a decimal point and to the right of a nonzero digit. 30.00 to the right of a decimal point and to the right of a nonzero digit. 30.00 to the left of an expressed decimal point and to the right of a nonzero digit. 19,000. to the left of an expressed decimal point and to the right of a nonzero digit. 19,000. Not significant when... Not significant when... the zeros to the right of a decimal and to the left of a nonzero digit. 0.00056 the zeros to the right of a decimal and to the left of a nonzero digit. 0.00056 to the right of a nonzero digit but to the left of an understood decimal 109,000 to the right of a nonzero digit but to the left of an understood decimal 109,000

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Beginning zeros are not significant. Beginning zeros are not significant. Ending zeros are only significant when there is a decimal. Ending zeros are only significant when there is a decimal.

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Operations with significant figures Multiplication and division Multiplication and division The answer contains the same number of significant figures as the measurement with the least number of significant figures. Addition and Subtraction Addition and Subtraction The answer has the same number of decimal places as the measurement with the least number of decimal places.

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Operations with significant figures Multiplication and division Multiplication and division Sample 1: 24 cm x 31.8 cm = 763.2 cm 2 answer: 760 cm 2 answer: 760 cm 2 Sample 2: 8.40 g ÷ 4.2 ml = 2 g/ml answer: 2.0 g/ml answer: 2.0 g/ml

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Addition and Subtraction Addition and Subtraction Sample 1: 49.1 g + 8.001 g = 57.101 g answer: 57.1 g answer: 57.1 g Sample 2: 81.350 m – 7.35 m = 74 m answer: 74.00 m answer: 74.00 m

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Precision vs. Accuracy Precision is the agreement between measurements. Precision is the agreement between measurements. Accuracy is the nearness of a measurement to its actual value. Accuracy is the nearness of a measurement to its actual value. x x x Precise and accuratePrecise, not accurate x Not precise, nor accurate

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These thermometers have different levels of precision. The increments on the left one are.2 but on the right one they are 1. How should their temperatures be recorded? 5.8 37.53

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Percent Error theoretical – experimental x 100% = theoretical theoretical Ex.: You analyze a sample of copper sulfate and find that it is 68% copper. The theoretical value is 80%. What is your percent error? 80-68 x 100% = 15% 80-68 x 100% = 15% 80 80

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Derived Units Measurements derived from basic units. Measurements derived from basic units. Area= L x W (m 2 ) Area= L x W (m 2 ) Volume = L x W x H (cm 3 ) Volume = L x W x H (cm 3 ) Density = m/V (g/cm 3 ) Density = m/V (g/cm 3 )

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Calculations 1. What is the density of a substance whose mass is 3.0 grams and its volume is 15cm 3 ? 3.0 grams =.20 g/cm 3 3.0 grams =.20 g/cm 3 15 cm 3 15 cm 3 2. Cobalt has a density of 8.90 g/cm 3. What volume would 17.8 g of cobalt have? D=m/V soV=m/D V = 17.8 g = 2.00 cm 3 8.90 g/cm 3 8.90 g/cm 3

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Dimensional Analysis Multiply your starting point by a conversion factor (equal to 1) Multiply your starting point by a conversion factor (equal to 1) Units should cross out algebraically, leaving you with the unit desired. Units should cross out algebraically, leaving you with the unit desired. Ex.: Convert 2hr to min. Conversion factor is 1hr = 60min 2hr x 60min = 120 min 1 hr 1 hr

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In Switzerland, gas prices are listed in Swiss Francs per liter. Convert the Swiss prices below to dollars per gallon.

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Conversion factors needed: Conversion factors needed: Dollars to Francs: 1 SF = $.83 Dollars to Francs: 1 SF = $.83 Liters to gallons: 1 quart = 0.946 L Liters to gallons: 1 quart = 0.946 L 1 gallon = 4 quarts 1 gallon = 4 quarts 1.71 SF x $.83 x.946L x 4 qt = $5.37 1 L 1 SF 1 qt 1 gal gal 1 L 1 SF 1 qt 1 gal gal

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