Dimensional Analysis

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During calculations, it is often necessary to convert between units. To do this, dimensional analysis (also called unit factor method) must be used.
For example, if we want to convert 10.83 inches in to centimeters, we would need an equivalence statement: 2.54 cm = 1 in. Now that we know 2.54 cm = 1 in, we can multiply 10.83 inches by 2.54 cm/in:
            2.54 cm
10.83 in x --------- = 27.51 cm (remember sig figs!)
             1 in
Notice how the inches units cancel out. Having units in calculations lets you know how things cancel out to arrive at the final answer. It is a good idea to always include units in calculations for this reason alone.

Here is another example of using dimensional analysis in calculations:
What is the mass of 8.7 cm3 of silver if the density of silver is 10.5 g/cm3?
First of all, you should consider what you want: the mass of the sample. In the information provided above, you see a mass unit (g) in the density 10.5 g/cm3. Secondly, you also see that both of the numbers given have the units cm3, which you don't want. Your aim is to cancel out the extraneous units and get the unit you want: g. 
           10.5 g
8.7 cm3 x -------- = 91 g
           1 cm3
Using dimensional analysis, you find that the sample of silver weighs 91 g.
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