Dimensional Analysis – Practice Problems



Dimensional Analysis – Practice Problems

Name: _______________________ Period: ______ Date: _____________

Two rules always apply:

• Quantities must have the same dimensions to be added or subtracted

• Dimensions on the left side of an equation must be equivalent to the dimensions on the right side of the equation

metric units

|basic unit |abbreviation |quantity measured |

|meter |m |length and distance |

|gram |g |mass |

|liter |L |volume |

|Celsius |C° |temperature |

|second |s |time |

prefixes for metric units of measurement

|symbol |prefix |is equal to |

|n |nano- |10-9 (billionth) |

|μ |micro- |10-6 (millionth) |

|m |milli- |10-3 (thousandth) |

|c |centi- |10-2 (hundredth) |

|k |kilo- |103 (a thousand) |

|M |mega- |106 (a million) |

|G |giga- |109 (a billion) |

conversions between U.S. and metric units

|U.S. System |Metric |U.S. System |Metric |

|1 mile (mi) |1.60 km |1 gal |3.7853 L |

|1 ft. |0.30 m |1 lb. |4.448 N |

|1 pt. |0.4732L |1 qt. |0.9463 L |

|1 in. |2.54 cm | | |

1. Convert 100m, the length of a well-known track event, to kilometers.

2. Convert 5.98X1024 kg, the mass of Earth, to milligrams, mg.

3. How many kilometers are in a 5.44 mile bicycle race?

4. Your friend in Peru is sending you a 20.5 N package. How much will it weigh in pounds?

5. In Canada, you pass a speed limit sign that says 75 km/h. What is the limit in mi/h ?

6. How many liters of milk are in 3.4 gal?

7. How many meters long is a 100 yd football field? (Remember that 1 yd. = 3 ft.)

8. The average U. S. female adult is 5’6” tall. How many centimeters is that?

9. A hand of bananas is a small bunch made up of 5 bananas (each bananas is called a finger). If a large bunch of bananas is made up of 10 hands, how many bananas does it contain?

A certain type of tree bears 73 individual pieces of fruit each year. You own an orchard that contains 120 of these trees.

10. How much fruit will the orchard produce each year?

11. The upkeep and care of the orchard costs you $850 a year. At what price will you have to sell each piece of fruit just to break even?

12. A supermarket sells milk in containers of various sizes and charges consumers by the liter. How much does a plastic jug of milk with a volume of 3.79 L cost if milk sells for $0.76 per liter?

13. You are pouring hot chocolate into cups for yourself and some friends. Calculate the number of cups of hot chocolate that you can pour from a pitcher if the pitcher’s volume is 4.3 L and the volume of each cup is 170 cm3. (1 cm3 = 1 mL)

14. A pie can be cut into 8 slices. What is the minimum number of pies you would need if you were to serve a slice of pie with each cup of hot chocolate in #13. How many slice of pie would be left over?

15. Suppose you are making a 650 km trip in a car. The car is able to travel an average distance of 54 km on 1.0 gallon of gasoline. How much will the trip cost if the price of gasoline is $3.98/gal?

16. 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 for a movie that lasts 1 hour and 45 minutes?

17. A family in your neighborhood is moving to another state, and you are helping them pack their books ahead of time. They have 755 books, and the average book has a mass of 3.5 kg. If a box can hold 49 kg, how many boxes will be needed?

18. A flight from Chicago to New York costs $1.24/km. If the distance between the two cities is 1075 km, what is the total cost of the flight?

19. The average adult Frenchman has a pant waist size of 87.63 cm. How many inches is that?

20. A landfill for a county with a population of 65,000 people has a volume of approx. 2.0 X 106 m3. If the county produces 6,2 X 107kg of garbage each year and the density of the garbage is assumed to be 410 kg/m3, how many years will it take to fill the landfill? (Remember density = mass / volume)

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