Solving problems in chemistry
requires careful manipulation of numbers and their associated units, a method
known as dimensional
analysis.

For example: What is the
volume of a 5.25-gram sample of a liquid having a density of 1.23 g/mL? The density
of the liquid can be used as a conversion
factor. For the liquid in the example, 1.23 grams are equal to 1.00 milliliter
(mL). When the numerator and denominator of a fraction are equal, the fraction
has a value of 1, meaning that we can multiply by it for the purpose of changing
units. The density conversion factor can be expressed in either of the following
two ways.

The one we choose to multiply
by depends on what units we want in our result. In this case we want an answer
in units of milliliters. So we choose the fraction on the right and multiply
it by the mass given in the problem.

Note that if we had chosen
the other version of the density conversion factor, we would have ended up with
a different number and also nonsensical units.

This illustrates the importance
of carrying units throughout a calculation. One way to check your work is to cancel units carefully to make sure that you arrive at an answer with the appropriate
units. When you end up with units that don't seem to have any reasonable physical
meaning to the problem, such as grams squared per milliliter, you will realize that you must
have made some sort of mistake. Go back and check your work.