• In the process, numbers and units are equally important.
   
• Conversion factors are:
   
  • Relationships that convert one unit to another.
     
  • Always a fraction equal to one.
   
• You know that any number multiplied by 1 is still that number!
   
• Multiply what is given by fractions equal to one to convert units. You will have the same ratio you started with!
   
• Always be sure the unit to be eliminated is correctly placed in the conversion factor.

  If the unit to be eliminated is in the numerator (on top) of the given information, then the unit must be placed in the denominator (on bottom) of the conversion factor.

  Since the numerator and denominator of any conversion factor are equal, they may be flipped as needed.

• The diagram below shows how to "set up" dimensional analysis problems in this class. The horizontal line represents "divide by", vertical lines represent "multiply by".

This Is How It's Done:

• Begin by writting down what is given in the problem.
  

• Draw a horizontal under it and one vertical line beside it.
  

• As you add a conversion factor, draw a line through the units that "divide out".
  

• Use as few or as many conversion factors as you need.
   
• When all units have been canceled except those needed for the final answer, you have worked the problem!
  

• Pick up your calculator and punch buttons to get the number.

 
Examples:

• Convert 5000 milliliters to liters. It is known that 1 liter = 1000 milliliter. This becomes the conversion factor needed to work the problem.
  

• Convert 65 miles/hour to meters/second.

  There are two different units in this problem. Treat them seperately. It does not matter which unit you solve first, as long as you complete its conversion before going to the other.

  You CANNOT convert two units with one fraction!!

  

  In the diagram above, the problem is solved with two conversion factors - the first changed hours to seconds, the second miles to meters.

  If you didn't know how many seconds are in an hour or how many meters are in a mile, you could use relationships you do know.

  • 1 hour/60 minutes . . . 1 minute/60 seconds
  • 5280 feet/1 mile . . . 12 inches/1 foot . . . 1 inch/2.54 centimeters . . . 100 centimeters/1 meter

  
  There would be more fractions in the solution (and more buttons to push), but the answer would be the same!

   

1. Use conversion factors from the SI system to do the following conversions:
   1. 2.4 meters to centimeters
   2. 65.5 centigrams to milligrams
   3. 5 liters to cubic decimeters
   4. The density of a substance is 2.7 g/cm³. What is the density of the substance in kilograms per liter?
2. A car is traveling 65 miles per hour. How many feet does the car travel in one second?
3. The density of water is one gram per cubic centimeter. What is the density of water in pounds per liter?
4. How many basketballs can be carried by 8 buses?
   • 1 bus = 12 cars
   • 3 cars = 1 truck
   • 1000 basketballs = 1 truck

Answers: 1a. 240 cm, 1b. 655 mg, 1c. 5 dm³, 1d. 2.7 kg/L, 2. 95 ft/sec, 3. 0.45 lb/L, 4. 32 000 basketballs