It is often necessary when working problems to have to convert from one unit to another. The easiest and safest way to do this is by writing out the conversion factor and multiplying the original unit by this conversion factor. Doing this allows you to check that you have the correct unit at the end. One of the most common mistakes made by students in general chemistry is incorrect unit conversion: it is worth the extra ten seconds on a test to write out the entire procedure!

For example, say you are given a problem with one measurement of 0.621 liter and the other parts of the problem call for a volume unit of cubic centimeters (cm³). You must convert liters to cm³, so first you should look up the conversion factor: 1 L = 1000 cm³
Next, write out the unit and multiply it by the coversion factor

0.621 L * 1000 cm³/1 L = 621 cm³

It may be necessary to use several conversion factors to get from the unit you have to the one you need. In this case, simply multiply all of them together and make sure that the intermediate units cancel out. For example, how many seconds are in a day? You know how many hours there are in a day, and how many minutes are in an hour, and how many seconds there are in a minute, so you can convert:

1 day*(24 hours/1 day)*(60 minutes/1 hour)*(60 seconds/1 minute) = 86,400 seconds

Example: A 747 cruises at 660 miles/hour. How fast is this in kilometers/second?

Solution: You need several conversion factors here. There are 1.609 km/mile, 60 minutes/hour and 60 seconds/minute. Setting these up so that we begin with units of miles/hour and ending with km/sec, we have

660 miles/hour*(1.609 miles/1 km)*(1 hour/60 minutes)*(1 minute/60 seconds) = 0.295 km/sec

Information provided by: http://learn.chem.vt.edu