What are Units and Why Are They Important?

We use conversion factors to convert one unit to another unit for the same dimension.

For example, let's convert a density of
1 g/cm3 to units of lbm/ft3.

A numerical result without units is not acceptable unless
the result is dimensionless.

Units can also guide you to the solution of a problem or help you determine if your solution is correct.

If the units are not correct, then your solution probably has an error.

Let's consider the water in a beaker again:

grams (g) or pounds mass (lbm)

Common units for mass:

Common units for density:

grams per cubic centimeter (g/cm3)
or pounds mass per cubic foot (lbm/ft3)
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Ch 1, Lesson B, Page 2 - What are Units and Why Are They Important?

• Units give us a way to quantify dimensions.  What is your mass in kg ?
How tall are you in feet ?
• Many students develop the bad habit of slapping units on their answers at the end of the problem.
• This seems ok, especially if you KNOW what units the answer must have.
• But, it is not ok.
• You should keep the units on every intermediate value that you calculate.
• In this way, your solution yields not just a numerical answer, but also the UNITS associated with the answer.
• THEN, you should compare the units that your solution produced with the units that you KNOW the answer should have.
• If the units work, then you have some basis to believe that your solution is correct.
• If the units from your solution are NOT the units you expected for the answer, then you have some indication that something went wrong in your solution.
• So, the next logical question is “How do you keep track of units as you work through a problem ?”
• I think it would be easier to show you how to do this than it would be to describe it !
• So, let’s consider a quick example.
• You probably know that the density of water at 0oC is 1 g/cm3.
• So, can you use this value to determine the density of water at 0oC in lbm/ft3 ?
• Yes, you can, if you know how to use unit conversions.