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## Homework: Dimensional Analysis

#### Unit Factor Conversions

 Linear Measure 2.54 cm = 1 in 12 in = 1 ft 5280 ft = 1 mi 0.3048 m = 1 ft 1 km = 0.621 mi 1 furlong = 660 ft 3 ft = 1 yd 0.0394 in = 1 mm
 Weight/Mass 1 stone = 14 lbs 1 lb = 0.4536 kg 1 oz = 16 drams 1 oz = 28.3 g 16 oz = 1 lb 2,000 lbs = 1 ton 1 oz = 28,350 mg 1 carat = 0.2 g
 Volumetric Measure 1 cup = 16 tablespoons 2 cups = 1 pint 2 pints = 1 quart 1 gal = 4 quarts 1 gal = 3.78 L 1 mL = 1 cm3 1 m3 = 1000 L 1 cup = 236.6 mL
 Time 1,000 ms = 1 s 60 s = 1 min 60 min = 1 hr 24 hr = 1 day 365 day = 1 yr 14 days = 1 fortnight 10 yr = 1 decade 100 yr = 1 century

Answer the following questions. If you get stuck on any one question feel free to skip to the next section and then come back to try again.

1. What is the weight in pounds of a 14 carat diamond?
2. Explain why there are not 12 square inches (in2) in 1 square foot (ft2).
3. Convert 4 m2 to in2.
4. Explain how to convert units when you have two units in a ratio such as in 25 mi/hr.
5. Convert 10 mi/hr to furlongs/fortnight.
6. Explain why 5 lbs 2 oz is not equal to 5.2 lbs.
7. Add together 5 lb 2 oz and 6 lb 15 oz and report your result as a decimal.
8. Convert 9 g/cm3 to kg/m3.

The questions continue on the back.

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Use dimensional analysis to solve the following problems. Show all work by including the following:

1. The unit equality (ex.: 12 in = 1 ft)
2. The number (w/unit) multiplied by the conversion factor obtained using the unit equality
3. Cancellation of the units
4. The answer showing the new unit
1. Your car needs fuel. The last time you filled the tank to the top you set the trip odometer to zero. Now the trip odometer reads 367.5 mi. When you fill the tank to the top this time you buy 12.598 gal of gasoline. How many miles per gallon does your car get?
2. How many miles per liter is that?
3. How many kilometers per liter is that?
4. Show how you would calculate the number of km/L from mi/gal in one dimensional analysis calculation.
5. If gas costs 4.15 dollars per gallon, how much does it cost to drive 1 mi? In other words, what is the cost to drive in dollars per mile?
6. You have graduated and have an opportunity to start working in your dream job. That job is 42 mi away. How much will the round trip cost you every day using the price for gas quoted above?
7. Now that you know the cost per day, what will it cost you per week to get to this job?
8. What will it cost per year, assuming that you work five days a week for 50 weeks? (You would be very lucky to get 2 full weeks of paid vacation in your first year on the job!)