Conversion, Units and Scientific Notation



Name _______________________ Period _____ Date ___________________

More Dimensional Analysis

Answer the following questions using these conversion factors:

1 inch = 2.54 cm

1 mile = 1609 meters

1 mile = 5280 feet

1 gallon = 3.78 liters

1 gallon = 231 in3

1 m3 = 1000 L

1 ton = 2000 pounds

1. Sally gets paid $8 per hour. If she works 8 hours per day, 5 days per week, how much will she earn in a year?

2. How tall is a 6 foot man in centimeters?

3. The world record holder in the 1600 meters can run the event in 4 minutes, 48 seconds. How fast is this in meters per second (m/s)?

4. The speed of sound is 761 mi/hr at sea level. How fast is this in m/s?

5. A swimming pool measures 3 x 10 x 2 meters.

a. How many liters of water will the pool hold?

b. How many gallons will it hold?

c. If your garden hose flows at 20 liters per minute, how long will it take to fill the pool?

6. The Indy 500 is a 500 mile race that is completed in about three hours.

a. What is the average speed of the cars that complete the race in miles per hour?

b. How fast is that in meters per second?

7. If 2 inches of rain fall on the roof of a 2000 square foot house, how many gallons of rain water could be collected?

8. Your cross country snow skis are 210 cm long. What is their length in inches?

9. As of today, Barry Bonds has hit 761 homeruns in his career in Major League Baseball. Given that there are 4 bases with 90 feet between each base, how many miles has he run just from home runs?

10. In Europe, gasoline is sold by the liter. Assume that it takes 14 gallons of gasoline to fill the tank of a compact car. How many liters would be in that same tank if it were half full?

11. How many miles could you drive for $7.90 if the gas mileage of your car is 14 km/liter of gas and the price is $2.79/gal? (1.61 km/mile, 4 qt/gal, 1.1 qt/L)

12. Dave operates a crane that can pick up 3.0 tons of excavated earth in an hour. Dave’s wages are $35 per hour. What, then, is the cost of picking up 500 pounds of excavated earth?

Bonus:

Because you never learned dimensional analysis in high school, you have been working at a fast food restaurant for the past 35 years wrapping hamburgers. Each hour you wrap 184 hamburgers. You work 8 hours per day. You work 5 days a week. You get paid every 2 weeks with a salary of $840.34. How many hamburgers will you have to wrap to make your first one million dollars? [You are in an impossible situation. If you can solve the problem, you will have learned dimensional analysis and you can get a better job. But, since you won't be working there any longer, your solution will be wrong. If you can't solve the problem, you can continue working which means the problem is solvable, but you can't solve it. We have decided to overlook this impasse and allow you to solve the problem as if you had continued to wrap hamburgers.]

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