Unit analysis or dimensional analysis is a method used to calculate values based on the units of each measurement. We will start by using this method to simply convert one measurement in one unit to another unit. This technique may seem more complicated than necessary at this point, but remember you are learning how to use the units. Later in the semester you will see that unit analysis will make problem solving so much easier!
Unit analysis is based on two very fundamental mathematical principles.
- any number multiplied by one is equal to itself
- a fraction equals one if the value of the numerator equals the value of the denominator
These two properties allow us to let the measurements determine how to do the calculation. The final answer must have the units desired and all other units must be canceled.
Changing both the unit in the numerator and the denominator is just like changing only one set of units. Just remember that all the units except the ones needed must cancel.
Change 3.40 m/sec to km/yr.
Notice that you must put the 60 sec in the numerator to cancel the sec you were given. All units must cancel except the ones requested in the problem. In this case, km/year.
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