 Converting Units

In many problems you must convert from one set of units to another. For example, from feet to centimeters, or miles per hour to feet per second. To do this, you set up a computation which involves the original parameter value along with its units and multiply by the conversion factors, along with their units, but you have to be careful that the units in the numerator cancel with the units in the denominator to give you the correct new units. This is just like reducing fractions except that it is units you are canceling instead of factors. This sounds complicated, but I'll give you a couple of examples that should clarify this concept:
• Convert 60 miles per hour to feet per second:
1. Here are the conversion factors involved:
• 5280 feet/mile
• 3600 seconds/hour
2. Write down the problem with the conversion factors:
60 miles x 5280 feet x   1   hour   =
hour         mile   3600 seconds

Notice that the seconds per hour factor is upside down so the units will cancel correctly

3. Cancel the units making sure the remaining units are the correct ones (feet/second)
60 miles x 5280 feet x  hour   =
hour         mile   3600 seconds

miles canceled miles and hour canceled hour leaving feet/second

4. Perform the calculation:
60  x 5280 feet    = 5280 = 88 feet
3600 second      60      second

• Convert 36 feet to centimeters:
1. Here are the conversion facors involved:
• 12 inches/foot
• 2.54 centimeters/inch
2. Write down the problem with the conversion factors:
36 feet x 12 inches x 2.54 centimeters =
foot             inch

3. Cancel the units making sure the remaining unit is the correct one (centimeters)
36 feet x 12 inches x 2.54 centimeters =
foot             inch

4. Perform the calculation:
36 x 12 x 2.54 centimeters = 1097.28 centimeters

 Now here's a problem for you: Convert 45 meters to yards! Use these conversion factors: 36 in/yard 2.54 cm/inch 100 cm/meter Hint: here's how these conversion factors combine to make yards: m x cm x in x yard ← See how these cancel to leave yards? m cm in Write down the problem with the conversion factors: (Some of them are upside-down!) Cancel the units making sure the remaining unit is the correct one (yards) Perform the calculation: