dimensional analysis
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Dimensional Analysis. Performing these conversions is a lot like going on a road trip. MATH IS THE LANGUAGE OF CHEMISTRY!!!. Scientific Notation. Scientist use special notation to express very large or very small numbers. Example I: 300,000,000 g can be written as… 3 x 10 8 g - PowerPoint PPT PresentationTRANSCRIPT
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Performing these conversions is a lot like going on a road trip.
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Converting Metric Measurementsbasic unitcenti-hecto-deca-kilo-deci-milli-110-110-310-2103102101To convert, move the decimal place the number of stairs you step on in the direction you are traveling. Example:3.75 km = ? mm? = 3,750,000 mm
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Use dimensional analysis when converting between other units.Ex: How many inches are in 1500 meters?
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Scientific NotationScientist use special notation to express very large or very small numbers.
Example I: 300,000,000 g can be written as3 x 108 g
Ex II: 1,007,000,000 sec can be written as 1.007 x 109 sec
Ex III: 0.000 000 000 004 76 mL can be written as 4.76 x 10-12 mL
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Significant Figures Atlantic - Pacific Rule:Decimal Present: Count from the Pacific side Decimal Absent: Count from the Atlantic sideStart counting at the first non-zero number and count until you reach the end of the number
Ex. I: 3.00700 Decimal Present Pacific (left) 6 sig. figs.Ex. II: 300,700Decimal Absent Atlantic (right) 4 sig. figs.
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Before we take this trip, lets review significant figures0.0034050 L ___________33.600 m___________7500.0 g___________47,900 mm___________7,000,000,001 miles ___________8.07 Hz___________Determine how many significant figures are in each of the following measurements.5553103
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More practice366.2 L ___________9,047,022 mg ___________12.76 g___________ 999.9 J___________Round the following measurements off so that they each contain 3 significant figures.366 L9,050,000 mg12.8 g1.00 x 103 JNotice this one must be in scientific notation to have 3 sig. figs.
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Significant Figures in CalculationsWhen 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 CalculationsWhen 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: 123.25 + 46.0 +86.257 = 255.507 = 255.5The answer is expressed as 255.5 since 46.0 has only one decimal place.
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Before we take this trip, lets review significant figures36.57 m / 3.21 s = ___________41.376g + 13.3g + 42.9g=___________5.67 m x 13.44 m___________(5.83 m/ 2.67 s) /2.1 s___________9.374 V x 6___________Perform the prescribed operations. Round your answers to the proper # of sig. figs. 11.4 m/s97.6 g76.2 m21.0 m/s260 VFrom now on, we will round all our answers to the correct # of significant figures.
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Lets say you want to travel from Oracle Jct to Casa Grande...You must travel through Tucson a two part trip.Now back to our road trip
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Rule: You must stay on the roads
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X
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Rule: You need a map. Sometimes the map can be in your head. But, not at first.
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OKLets talk about making maps and solving conversion problems. The method we use is called the Factor-Label method, a.k.a. dimensional analysis.
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gallonskildurkinsFor Example: Given 1 kildurkin = 18 gallonsThis is our map.
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gallonskildurkinsFor Example: Given 1 kildurkin = 18 gallonsHow many kildurkins is 14 gallons?1 kildurkins18 gallons14 gallons=0.78 kildurkins
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General Format...going tocoming fromgiven
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gallonskildurkinsAlso given: 2 farkins = 1 kildurkinfarkinsLets expand the map...
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gallonskildurkinsAlso given: 1 hogshead = 63 gallonsfarkinshogshead1 barrel = 3.3 bushelsbushelbarrel1 bushel = 8 gallons
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gallonskildurkinsfarkinshogsheadbushelbarrelNow, Lets solve a problem.How many hogsheads are 14 barrels?Given: Start HereFinish HereThe trip will require 3 transitions123
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gallonshogsheadbushelbarrelHow many hogsheads are 14 barrels?123Given14 barrels3.3 bushels1 barrel8 gallons1 bushel1 hogshead63 gallons= 5.9 hogsheads
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gallonskildurkinsfarkinshogsheadbushelbarrelNow you try one. How many farkins is 3.00 bushels?Start HereEnd HereThis will require 3 Conversions.
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bushelsgallonskildurkinsfarkins3.00 bushels8 gallons1 bushel1 kildurkin18 gallons2 farkins1 kildurkin= 2.67 farkins
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Wow! How Cool Is That!