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## 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 expressvery largeorvery smallnumbers. Example I: 300,000,000 g can be written as… 3 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 side Start 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: 300,700 Decimal Absent… Atlantic (right)… 4 sig. figs.**Before we take this trip, let’s review significant**figures… Determine how many significant figures are in each of the following measurements. • 0.0034050 L ___________ • 33.600 m ___________ • 7500.0 g ___________ • 47,900 mm ___________ • 7,000,000,001 miles ___________ • 8.07 Hz ___________ 5 5 5 3 10 3**More practice…**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.**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.**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: 123.25 + 46.0 +86.257 = 255.507 = 255.5 The answer is expressed as 255.5 since 46.0 has only one decimal place.**Before we take this trip, let’s review significant**figures… Perform the prescribed operations. Round your answers to the proper # of sig. figs. • 36.57 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 ___________ 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.**Now back to our road trip…**Let’s say you want to travel from Oracle Jct to Casa Grande... You must travel through Tucson… a two part trip.**Rule: You need a map. Sometimes the map can be in your**head. But, not at first.**OK…Lets talk about making maps and solving conversion**problems. The method we use is called the “Factor-Label” method, a.k.a. dimensional analysis.**For Example: Given 1 kildurkin = 18 gallons**kildurkins gallons This is our map.**For Example: Given 1 kildurkin = 18 gallons**kildurkins gallons How many kildurkins is 14 gallons? 14 gallons 1 kildurkins =0.78 kildurkins 18 gallons**General Format...**given going to coming from**Let’s expand the map...**Also given: 2 farkins = 1 kildurkin kildurkins farkins gallons**Also given: 1 hogshead = 63 gallons**1 barrel = 3.3 bushels hogshead 1 bushel = 8 gallons kildurkins farkins gallons barrel bushel**Now, Lets solve a problem.**How many hogsheads are 14 barrels? Finish Here hogshead 3 kildurkins farkins gallons 2 barrel bushel Given: Start Here 1 The trip will require 3 transitions**How many hogsheads are 14 barrels?**hogshead Given 3 gallons 14 barrels 3.3 bushels 8 gallons 1 hogshead 63 gallons 1 barrel 1 bushel 2 = 5.9 hogsheads barrel bushel 1**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.**farkins**bushels gallons kildurkins 8 gallons 3.00 bushels 1 kildurkin 2 farkins 1 kildurkin 1 bushel 18 gallons = 2.67 farkins