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Unit 1 Scientific Notation/Powers of 10 Significant Figures
Dimensional Analysis (Factor Label Method)
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MATH IS THE LANGUAGE OF CHEMISTRY!!!
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Scientific Notation Scientist use special notation to express very large or very small numbers. Example I: 300,000,000 m/sec can be written as… 3 x 108 m/sec Ex II: 1,007,000,000 sec can be written as… 1.007 x 109 sec Ex III: m can be written as… 4.76 x m
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Converting Metric Measurements (PART 4 of Things to Know and Love)
To convert, move the decimal place the number of stairs you step on in the direction you are traveling OR use dimensional analysis. kilo- 103 hecto- 102 deca- basic unit 101 1 deci- Example: 3.75 km = ? mm 10-1 centi- 10-2 milli- ? = 3,750,000 mm 10-3
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SIGNIFICANT FIGURES Scientists indicate the precision of measurements by the number of digits they report = sig. figs. A value of 3.52 g is more precise than a value of g All known digits plus one estimated digit ** the equipment used for a measurement will determine the number of sig. figs.
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Significant Figures Atlantic - Pacific Rule:
Decimal Present: Count from the Pacific side Decimal Absent: Count from the Atlantic side Start counting at the first non-zero number and count until you reach the end of the number Ex. I: Decimal Present… Pacific (left)… 6 sig. figs. Ex. II: 300,700 Decimal Absent… Atlantic (right)… 4 sig. figs. (the last 2 zeros are PLACE HOLDERS)
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5 (the first 3 zeros are PLACE HOLDERS) 0.0034050 L ___________
REVIEW Determine how many significant figures are in each of the following measurements. 5 (the first 3 zeros are PLACE HOLDERS) L ___________ m ___________ g ___________ 47,900 mm ___________ 7,000,000,001 miles ___________ 8.07 Hz ___________ 5 5 3 (the last 2 zeros are PLACE HOLDERS) 10 3
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More practice… 366.2 L ___________ 366 L 9,047,022 mg ___________
Round the following measurements off so that they each contain 3 significant figures. 366.2 L ___________ 9,047,022 mg ___________ 12.76 g ___________ 999.9 J ___________ 366 L 9,050,000 mg 12.8 g 1.00 x 103 J Notice this one must be in scientific notation to have 3 sig. figs.
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Significant Figures in Calculations
When multiplying and dividing, limit and round to the least number of significant figures in any of the factors. Example: 23.0 x 432 x 19 = 188,784 = 190,000 The answer is expressed as 190,000 or 1.9 x 105 since 19 has only two sig. figs.
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Significant Figures in Calculations
When adding and subtracting, limit and round your answer to the least number of decimal places in any of the numbers involved in the calculation. Example: = = 255.5 The answer is expressed as since 46.0 has only one decimal place.
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REVIEW Perform the prescribed operations. Round your answers to the proper # of sig. figs. 36.57 m / 3.21 s = ___________ 41.376g g g=___________ 5.67 m x m ___________ (5.83 m/ 2.67 s) /2.1 s ___________ 9.374 V x 6 ___________ 11.4 m/s 97.6 g 76.2 m2 1.0 m/s2 60 V From now on, we will round all our answers to the correct # of significant figures.
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EXTRA REVIEW Using a calculator for EXPONONETS Example 1:
(EE, EXP or x10x button) Example 1: (5.02 x 10-3) x ( x 105) = *put in correct sig figs = 3 sig figs = 3180 or 3.18 x 103
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Example 2 (use EE button!)
(2.99 x 106) x (2.334 x 10-3) = = 3 sig figs 6980
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DIMENSIONAL ANALYSIS How old are you in seconds?
Go from number of years to number of seconds. EX: 15 years old _____ seconds old. To do this, you need to use CONVERSION FACTORS (a ratio of equivalent values used to express the same quantity in different units)
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Performing these conversions is a lot like going on a road trip.
Dimensional Analysis Performing these conversions is a lot like going on a road trip.
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ROAD TRIP!!! Let’s say you want to travel from Oracle Jct to Casa Grande... You must travel through Tucson… a two part trip.
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Rule: You must stay on the roads & REMEMBER SIG FIGS!!!
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DO NOT GO OFF ROAD! X
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Rule: You need a map. Sometimes the map can be in your head
Rule: You need a map. Sometimes the map can be in your head. But, not at first. (show all work!!)
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GIVEN INFORMATION 1 kildurkin = 18 gallons 2 farkins = 1 kildurkin
1 hogshead = 63 gallons 1 barrel = 3.3 bushels 1 bushel = 8 gallons
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Make a UNIT CONVERSION MAP
Draw connections between the units in the conversion factors… (as you draw connections, check that conversion factor off the list) It’s kind of like a road map…
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hogshead kildurkins farkins gallons barrel bushel
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General Format... given going to = X coming from
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Let’s calculate Convert 14 gallons to kildurkins
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Convert 14 barrels to hogshead
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Convert 3.00 bushels to farkins
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Now you try one. How many farkins is 3.00 bushels?
End Here hogshead kildurkins farkins gallons Start Here barrel bushel This will require 3 Conversions.
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= 2.67 farkins bushels gallons kildurkins farkins 8.0 gallons
X X X 1.0 bushel 18 gallons 1.0 kildurkin = 2.67 farkins
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Wow! How Cool Is That!
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Handout: Fun Factor Label
Piece of lined paper (landscape format) Front is web for Distance and back is for Vol. Conversion Factors: change to x 10-10 Let’s do league km m cm to start You finish web, then do #3,6,7,9 Then do vol. web Then finish questions #4, 5, 8, 10 FINISH FOR HW
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