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Dimensional Analysis

Performing these conversions is a lot like going on a road trip.

MATH IS THELANGUAGE OFCHEMISTRY!!!

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 mmUse dimensional analysis when converting between other units.Ex: How many inches are in 1500 meters?

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

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.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.5553103More 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.

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. 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. 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.

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

Rule: You must stay on the roads

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Rule: You need a map. Sometimes the map can be in your head. But, not at first.

OKLets talk about making maps and solving conversion problems. The method we use is called the Factor-Label method, a.k.a. dimensional analysis.gallonskildurkinsFor Example: Given 1 kildurkin = 18 gallonsThis is our map. gallonskildurkinsFor Example: Given 1 kildurkin = 18 gallonsHow many kildurkins is 14 gallons?1 kildurkins18 gallons14 gallons=0.78 kildurkinsGeneral Format...going tocoming fromgivengallonskildurkinsAlso given: 2 farkins = 1 kildurkinfarkinsLets expand the map...gallonskildurkinsAlso given: 1 hogshead = 63 gallonsfarkinshogshead1 barrel = 3.3 bushelsbushelbarrel1 bushel = 8 gallons

gallonskildurkinsfarkinshogsheadbushelbarrelNow, Lets solve a problem.How many hogsheads are 14 barrels?Given: Start HereFinish HereThe trip will require 3 transitions123gallonshogsheadbushelbarrelHow many hogsheads are 14 barrels?123Given

14 barrels3.3 bushels1 barrel8 gallons1 bushel1 hogshead63 gallons= 5.9 hogsheadsgallonskildurkinsfarkinshogsheadbushelbarrelNow you try one. How many farkins is 3.00 bushels?Start HereEnd HereThis will require 3 Conversions.bushelsgallonskildurkinsfarkins3.00 bushels8 gallons1 bushel1 kildurkin18 gallons2 farkins1 kildurkin= 2.67 farkins

Wow! How Cool Is That!