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Dimensional Analysis

Dimensional Analysis. DHS Chemistry ferrer. Setting Up Ratios. 100 centimeters = 1 meter can be written as 100 cm OR 1 m___ 1 m 100 cm 8 slices = 1 pizza can be written as 1 pizza OR 8 slices___ 8 slices 1 pizza.

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Dimensional Analysis

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  1. Dimensional Analysis DHS Chemistryferrer

  2. Setting Up Ratios • 100 centimeters = 1 meter can be written as • 100 cm OR 1 m___ • 1 m 100 cm • 8 slices = 1 pizza can be written as • 1 pizza OR 8 slices___ • 8 slices 1 pizza

  3. The Format • # x # x # x # = • 1 # # # • OR • # # # = • 1 # # • Note: Unless you are using 1 as a spot filler, all numbers should ALWAYS include units

  4. Understanding order of operations & typing in calculator keys correctly • Solve. 10 13 6 = 2 4 • Method 1: 10 X 13 X 6 = 780 then divide 97. 5 2 x 4 = 8 • Method 2: 10 X 13 X 6 / 2 / 4 = 97.5 130 780 390 97.5 • Method 3: 10 X 13 / 2 X 6 / 4 = 97.5130 65 390 97.5

  5. Try It • 15 2 3 1.2 4 = • 1 4 5 14 5 • 0.308

  6. Canceling out units • Just as numbers are multiplied and divided, units are too. Cancel out all units that are located in both the numerator and denominator to reveal the left over units. • cm in feet yard = yard cm in feet

  7. Try It • week day hr min sec = sec • 1 week day hr min

  8. Putting the numbers & units together • 3 weeks 7 day 24 hr 60 min 60 sec = • 1 1 week 1 day 1 hr 1 min =1814400 sec Rules?

  9. I. One-Step Conversions

  10. I. One- Step ConversionsEX 1: Determine the number of slices in 282.3 pizzas • Step 1) what are you given? • Step 2) What are you trying to get? • Step 3) List your relationships • (remember from pg 1 of the notes) • Step 4) Set up your problem 282.3 pizzas Number of slices 1 pizza = 8 slices 282.3 pizzas 8 slices slices =2258.4 1 1 pizza

  11. EX 2: Determine the number of dozen eggs in 3.8 x 103 eggs. • Step 1) what are you given? 3.8 X 103 eggs • Step 2) What are you trying to get? Dozen eggs • Step 3) List your relationships • 12 eggs = 1 dozen • Step 4) Set up your problem These should match 1 dozen 3.8 X 103 eggs Dozen of eggs =317 1 12 eggs

  12. Practice • Determine the number of feet in 2821 inches. Relationship1 foot = 12 inches want given Start with what’s given 2821 in 1 foot feet = 235 1 12 in

  13. Practice • 2. Determine the number of g in 0.03455 kg Relationship1000g = 1kg want given Start with what’s given 0.03455 kg 1000 g g = 34.6 1 1 kg

  14. given want Relationships1 mi = 1609.3 meter 1 mi = 1.6093 km Start with what’s given 37 mi 1.6093 km = 59.5 km 1 mi 1 99 mi 1.6093 km = 159 km 1 mi 1

  15. Solving the same problem, but in a different way

  16. given want Relationships1 mi = 1609.3 meter 1 km = 1000 m Start with what’s given 37 mi 1609.3 m 1 km = 59.5 km 1 mi 1 1000 m

  17. For every problem, start with: • Given: • Want: • Relationships:

  18. II. Multi-Step Conversions

  19. Given: Want: Relationships: 0.115 km • Ex. 1 Convert 0.115 km to cm ____ cm 100 cm = 1 m 1 km = 1000 m

  20. Relationships 1km = 1000m 100cm = 1m given want • Ex. 1 Convert 0.115 km to cm Start with what’s given 0.115 km 1000 m 100 cm 1 m 1 km 1 cm = 1.15 x 104

  21. Given: Want: Relationships: 323 mL • Ex. 2 Convert 323 mL to cups ____ cups 1000 mL = 1 L 1 L = 1.06 quarts 1 quart = 4 cups

  22. Relationships 1000 mL = 1L 1L = 1.06 quarts 1 quart = 4 cups given want • Ex. 2 Convert 323 mL to cups Start with what’s given 4 cups 1.06 qt. 323 mL 1 L 1 L 1000 mL 1 1 qt. cups = 1.37

  23. Given: Want: Relationships: 7.005 ft • Practice 1: Convert 7.005 ft to mm ____ mm 1 foot = 12 inches 1 inch = 2.54 cm 100cm = 1 m 1m = 1000mm

  24. Relationships 1 foot = 12 inches 2.54cm = 1 in 100 cm = 1 m 1 m = 1000 mm given want • Practice 1: Convert 7.005 ft to mm Start with what’s given 1000 mm 12 in 2.54 cm 1 m 7.005 ft 1 1 ft 1 in 100 cm 1 m = 2135 mm

  25. Given: Want: Relationships: 2 years • Practice 2: calculate the number of seconds in 2 years ____ seconds 1 year = 365.25 days 24hrs = 1 day 60 min = 1 hr 1 min = 60 sec

  26. Relationships 1 year = 365.25 days 1 day = 24 hours 1 hr = 60 min 1 min = 60 sec given want • Practice 2: calculate the number of seconds in 2 years Start with what’s given 60 sec 24 hrs 60 min 2 years 365.25 days 1 1 year 1 day 1 hr 1 min = 6.31 X 10 7 seconds

  27. What does that price mean? $1.99 = 1lb

  28. III. Combination Unit Conversions

  29. Writing Clean Fractions • Take the following quantities and turn it into a clean fraction as if you were starting a dimensional analysis problem. • 36.0 m/s 36.0 m OR s ___ • s 36.0m • 722 mi/hr 722 mi OR hr__ • hr 722mi

  30. Writing clean fractions from the denominator • Remember from algebra, that a fraction in the denominator can be multiplied by its reciprocal. Take the following quantities and turn it into a clean fraction as if you were starting a dimensional analysis problem. • 52m to 52m s = 0.0715 s 727m/s 1 727m • 46mi to 46 mi hr = 0.767 hr 60mi/h 1 60mi

  31. Given: Want: Relationships: 0.083 km/hr • EX 1: Convert 0.083 km/hr to m/s ____ m/s 1 km = 1000m 1 hr = 60 min 1 min = 60 sec

  32. Relationships1km = 1000m 1h = 60 min 1 min = 60 s given want • EX 1: Convert 0.083 km/h to m/s Start with what’s given 1000m 1 hr 1 min 0.083km 1hr 1 km 60 min 60 s m/s = 2.31 X 10-2

  33. Given: Want: Relationships: 2.85 g/mL • EX 2: Convert 2.85 g/mL to lb/gal ____ lbs/gal 454g = 1lbs 1 gal = 4 quarts 1.06 qts = 1L 1 L = 1000mL

  34. Relationships454 g = 1lb • 1000mL = 1 L • 1.06qt = 1 L • 4 qt = 1 gal given want • EX 2: Convert 2.85 g/mL to lb/gal Start with what’s given 1 L 4 qt 1lb 1000mL 2.85 g 1 L 1mL 454 g 1.06 qt 1 gal = 23.7 lb/gal

  35. Given: Want: Relationships: 3.56 cm/s • 1. Convert 3.56 cm/s to ft/hr ____ ft/hr 1 ft = 12 in 2.54 cm = 1 in 1 hr = 60 min 1 min = 60 sec

  36. Relationships2.54 cm = 1 in • 12 in = 1 ft • 60 s = 1 min • 1 hr = 60 min want • 1. Convert 3.56 cm/s to ft/h given Start with what’s given 1 in 1 ft 60 s 60 min 3.56 cm 1 s 2.54 cm 12 in 1 min 1 hr = 420 ft/hr

  37. Given: Want: Relationships: $25.00/ft • 2. Convert $25.00/feet to cents/cm ____ cents/cm $1.00 = 100 cents 1 ft = 12 inches 2.54 cm = 1 in

  38. Relationships$1 = 100 cents • 2.54 cm = 1 in • 12 in = 1 ft given want • 2. Convert $25.00/feet to cents/cm Start with what’s given 1 in 100 cents 1 ft $ 25.00 12 in 1 ft $1 2.54 cm = 82.0 cents/cm

  39. Solving Word Problems using Dimensional Analysis

  40. If you are given multiple numbers in a problem, only one number will be your starting point. The other numbers are relationships that you will use in your problem. If you are given multiple numbers and one of them involves a “/” (e.g. m/s), then always use the “/” as a relationship and start with the other number.

  41. If it helps, change any combination unit into a relationshipex. 0.05mL/s0.05mL = 1 s

  42. Given: Want: Relationships: 0.05mL/s • EX: A faucet is dripping at a rate of 0.05 mL/s. How many liters of water will be lost in 1 day? 1 day ____ Liters 0.05mL = 1 sec 1000mL = 1 L 60 sec = 1 min 1 day = 24 hr 1 hr = 60 min

  43. Relationship want given • EX: A faucet is dripping at a rate of 0.05 mL/s. How many liters of water will be lost in 1 day? • Relationships0.05 mL = 1 s 60 min = 1 hr • 1000mL = 1 L 24 hr = 1 day • 60s = 1 min Start with what’s given 1 L 60 min 60 s 0.05 mL 1 day 24 hr 1 hr 1000 mL 1 1 day 1 min 1 s = 4.32 L

  44. Finally, note dimensional analysis can be used anytime you can say something is equal to something else. It does not have to involve standard conversion factors.

  45. EX 1: Motion pictures are shown at a speed of 24 frames, or individual pictures, each second. If a standard frame is 1.9 cm long, how long will the strand of film be (in ft) for a 2 ½ hr movie? Given: Want: Relationships: 2.5 hours ____ feet 24 frames = 1 sec 1 hr = 60 min 1 in = 2.54cm 1 frame = 1.9cm 1 min = 60 sec 1 ft = 12 in

  46. Relationship relationship want • EX 1: Motion pictures are shown at a speed of 24 frames, or individual pictures, each second. If a standard frame is 1.9 cm long, how long will the strand of film be (in feet) for a 2 ½ hour movie? want given • Relationships24 frames = 1 s1 frame = 1.9cm • 1 hr = 60 min 60 s = 1 min • 1in = 2.54 cm 1 ft = 12 in Start with what’s given 2.5 hr 60 s 24 frames 1.9 cm 1in 1 ft 60 min 1 min 12 in 1 1 hr 1 s 1 frame 2.54 cm = 13464.6 ft

  47. Given: Want: Relationships: • 1. The Toyota Prius gets 60 mi/gal of gas. If each trip to school is 3.5 km, how many trips can I make with 10 gallons of gas? 10 gallons ____ trips 60 mi = 1 gal 1 trip = 3.5km 1000m = 1km 1 mile = 1609.3 m

  48. Relationship relationship want • 1. The Toyota Prius gets 60 mi/gal of gas. If each trip to school is 3.5 km, how many trips can I make with 10 gallons of gas? given • Relationships60 miles = 1 gal1 trip = 3.5 km • 1 mi = 1609.3m 1000m = 1km Start with what’s given 10gal 1609.3 m 1 km 1 trip 60 mi 1 mi 1000m 1 1 gal 3.5 km = 276 trips

  49. 2. Every second 2500 g of sulfuric acid flows out of a pipe. How many kg of sulfuric acid will flow in 1 day? Given: Want: Relationships: 1 day ____ kg 1 sec = 2500g 1kg = 1000g 60 s = 1 min 60 min = 1 hr 24 hrs = 1 day

  50. Relationship want • 2. Every second 2500 g of sulfuric acid flows out of a pipe. How many kg of sulfuric acid will flow in 1 day? given • Relationships1 s = 2500g 60s = 1 min • 1000g = 1kg 60 min = 1 hr • 24 hr = 1 day Start with what’s given 1 day 60 min 60 s 2500g 1 kg 24 hr 1 hr 1 min 1 s 1 1 day 1000g = 216000 kg

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