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Published byPhillip Mathews Modified over 8 years ago
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Course Outline
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Math Review
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Measurement Using Measurements
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Accuracy vs Precision Accuracy: Precision: How close a measurement is to the actual size of the object. How close a series of measurements are to each other. ACCURATE = CORRECT PRECISE = CONSISTENT
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Significant Figures Indicate precision of a measurement. Recording Sig Figs: Sig figs in a measurement include the known digits plus a final estimated digit. Your answer you record can only ever be as accurate as the question. 2.35 cm
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Significant Figures Counting Sig Figs (See Handout) As a general rule, your answer should have the same number of sig figs as the number in the question with the lease sig figs. Count all numbers EXCEPT: Leading Zeroes--0.0025 2 Sig Figs
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Significant Figures Counting Sig Figs Examples Practice 23.50 1. 4 Sig Figs 2.402 3 Sig Figs 3. 5,280 4 Sig Figs 4. 0.080 2 Sig Figs
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Significant Figures Calculating With Sig Figs Multiply/Divide The # with the fewest sig figs determines the # of sig figs in the answer (13.91 g/cm 3 ) 4 Sig Figs (23.3 cm 3 ) 3 Sig Figs = 324.103g 3 Sig Figs 324 g
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Significant Figures Calculating With Sig Figs (continued) Add/Subtract The # with the lowest decimal value determines the place of the last sig figs in the answer. 3.75 mL + 4.1 mL 7.85 mL 7.9 mL
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Significant Figures Calculating With Sig Figs (continued) Exact Numbers The exact numbers do not limit the # of sig figs in the final answer. Example: 12 Students in a class. 1 Meter. 12.0000000000 1.0000000000
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Significant Figures Practice Problems 1. (15.30 g) ÷ (6.4 mL) 2. 18.9 g - 0.84 g 4 S.F 2 S.F = 2.390625 g/mL ~ 2.4 g/mL 2 S.F 18.06 g 18.1 g
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Scientific Notation 65,000 kg 6.5 X10 4 kg Converting into Scientific Notation: You take the number and move the decimal however many spots it takes until you have #.####### 1 # in front of decimal, and the rest behind. However number of spots you moved the decimal becomes the X 10 something General Rule: Large # (>>>1) Positive exponent on 10 1 or bigger Small # (<<<1) Negative exponent on 10 -1 or smaller
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Scientific Notation 6,300,400 km Examples: 123 4 56 = 6.3 X10 6 km 8.5 X 10 -7 L= 85 L 1 00 23 4 5 67 00000
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Scientific Notation Practice Problems: 1. 2,400,000 μg 2. 3. 4. 0.00256 kg 7 X 10 -5 km 6.2 X 10 4 mm 2.4 X 10 6 μg 2.56 X 10 -3 kg 0.00007 km 62,000 mm
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Scientific Notation Calculating with Sci. Notation (95.44 X 10 7 g) ÷ (8.1 X 10 4 mol) Type on your calculator: (5.44 X 10 ^ 7) ÷ (8.1 X 10 ^ 4) = 671.6049383 ~ 6.7 X 10 2 g mol
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Notice We can only add and subtract numbers with the same units. However, when we divide the units are divided And when we multiply the units are multiplied. Ex: 100km / 1 hour = 100km/hr ex: 5.0m * 2.0m = 10m 2
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Measurement Unit Conversions
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SI Prefix Conversions 1.Find the difference between the exponents of the two prefixes. 2. Move the decimal that many places.
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SI Prefix Conversions Prefix Symbol Factor mega kilo BASE UNIT deci- centi- milli- micro- nano- pico- M k d c m μ n p --- 10 6 10 3 10 0 10 -1 10 -2 10 -3 10 -6 10 -9 10 -12 Move decimal to the left. Move decimal to the right.
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Practice Problems 1)20cm = ___________meters 2)0.032 L = _____________mL 1)45 μm = ______________nm 1)805 dm = _____________km 32 0.2 45000 0.0805
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Dimensional Analysis The “Factor-Label Method Units or Labels are canceled out After you cancel out all the “repeated” units, you are left with the units you use in your answer.
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Dimensional Analysis The “Factor-Label Method Units or Labels are canceled out After you cancel out all the “repeated” units, you are left with the units you use in your answer.
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Dimensional Analysis 1cm 3 X 4 g = 1cm 3 4 g
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Cross Multiply and Divide X X 4 g = 1cm 3 4 g 4 X 1 = 4 ÷ 1 = 4
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Identify starting & ending units. Line up conversion factors so units cancel. Multiply all top numbers & divide by each bottom number. Cross multiply and divide Check units & answer
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Practice Problems How many milliliters are in 0.946 Liters of milk?
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Practice Problems How many milliliters are in 0.946 Liters of milk? 10 -3 = 1000 so….. 1000 ml/1L
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Practice Problems How many milliliters are in 0.946 Liters of milk? 0.946L x 1000ml/L = Use your calculator or just move the decimal 3 spots to the right. 946ml 3 Sig Figs ~ 946ml
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Practice Problems A roll of wire is 1.3 M long. How many 1.5 cm long pieces can you cut from the roll? Well first we need the same units. So convert both to centimeters or both to meters.
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Practice Problems A roll of wire is 1.3 M long. How many 1.5 cm long pieces can you cut from the roll?
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Practice Problems A roll of wire is 1.3 M long. How many 1.5 cm long pieces can you cut from the roll? 10 2 = 100 So…. 1m = 100cm
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Practice Problems A roll of wire is 1.3 M long. How many whole 1.5 cm long pieces can you cut from the roll? 1.3m X 100cm/m =130cm. 130 cm ÷ 1.5 cm/ piece = 86.666666666667 pieces ~ 86 pieces
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