Dimensional Analysis
dimensions: the units that something is measured in.
dimensional analysis: using the units (dimensions) to figure out (analyze) what the formula should be, or using the formula to analyze what the dimensions (units) should be.
For example, density is how heavy something is for its size. The formula is:
or 
From the formula, the units for density are therefore any mass unit divided by any volume unit. Some of the units that density could be measured in might include:
You can use dimensional analysis to help you figure out how to solve problems.
For example, if you wanted to know how many miles per hour you would have to drive to get from Waltham Center to downtown Boston in 15 minutes.
Google
directions says the route is 13 miles long. Speed is measured in 
, so the
units tell us that you need to divide miles by hours to get 
.
We have minutes, not hours, so we need to
1. convert 15 minutes to hours
2. divide 13 miles by this number of hours
The unit conversion would look like this:
,” or
“the car was going 
,” or “the gas had a molar
volume of 
.” Each of these is a temporary
conversion factor that you can use to convert from what you’re given to
what the problem is asking for. If a substance “has a density of 
,” it
means that for this substance, 
, and you can use that
conversion factor to convert between g and 
in this problem. If a car
“was going 
in the
problem. If a gas “has a molar volume of 
,” it means 
.