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| Given Quantity | Conversion | Result |
|---|---|---|
| 2 hours | 2 hours * 60 minutes/1 hour | 120 minutes |
Although the final result is in minutes, both quantities represent the same amount of time. Note that the opposite conversion, from minutes to hours, has a conversion factor of 1 hour60 minutes. If the task was to convert 120 minutes to hours, 120 minutes would be multiplied by this conversion factor.
| Given Quantity | Conversion | Result |
|---|---|---|
| 120 minutes | 120 minutes * 1 hour/60 minutes | 2 hours |
As shown in the examples above, the process of including units of measurement as factors is called dimensional analysis. Dimensional analysis can also be used when deciding which conversion factor will produce the desired units. In the table, some common conversion factors are used to convert the given measures.
| Given Quantity | Conversion | Result |
|---|---|---|
| 3 pounds | 3 pounds * 16 ounces/1 pound | 48 ounces |
| 160 ounces | 160 ounces * 1 pound/16 ounces | 10 pounds |
| 1 mile | 1 mile * 1760 yards/1 mile | 1760 yards |
The numerator and denominator of the conversion factor represent the same quantity. That means their quotient equals 1. Then, by the Identity Property of Multiplication, the amount of the given quantity does not change when multiplied by the conversion factor.
When converting from one unit to another, the desired unit needs to be in the numerator of the conversion factor while the given unit needs to be in the denominator. That way when the quantity is multiplied by the conversion factor, the given unit will cancel out and the desired unit will remain.
Keep in mind that, despite the given quantity and the new quantity have different values, they represent the same amount.