Analysis—The Factor Label Method

Dimensional analysis, sometimes called the factor label (unit conversion) method, is a method for setting up mathematical problems. Mathematical operations are conducted with the units associated with the numbers, and these units are cancelled until only the unit of the desired answer is left. This results in a setup for the problem. Then the mathematical operations can efficiently be conducted and the final answer calculated and rounded off to the correct number of significant figures. For example, to determine the number of centimeters in 2.3 miles  

write down the initial data as a fraction  

The answer will be rounded off to 2 significant figures based upon the 2.3 miles, since all the other numbers are exact  

Sometimes on the AP exam, only setups will be given as possible answers. Write the correct setup to the problem and then see which one of the answers represents your answer. 

Also Make sure that the answer is legible and reasonable  

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Multiplication by unity (by one) does not change the value of an expression. If we represent one in a useful way, we can do many conversions by just multiplying by one. This method of performing calculations is known as dimensional analysis, the factor-label method, or the unit factor method. Regardless of the name chosen, it is a powerful mathematical tool that is almost foolproof. 

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