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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)

Lesson
1B Blog

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Lesson 1B: page 2 of 14

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.

What are Units and Why Are They Important?

Ch 1, Lesson B, Page 2 - What are Units and Why Are They Important?