14.1: The importance of Units


When working with engineering and science it is important to keep an eye on your units. This is a theme that professors are always harping on, but with seemingly little success. This might be because when assignments or tests are time constrained it seems like something you can skip. This is not TRUE. Don't skip your units check. In real life always be very careful with your units, but for a time constrained tests you need to develop a fast method to check units which usually involve various shortcuts (these shortcuts depend on the individual so that will not be discussed here, but you certainly can find many shortcut methods in the various test prep books out there - note these shortcut methods are to only be used for tests, never when it matters the most, like when you are building the bridge we or your or our family members are going to drive my car on).

First let us have a review of units which is to say let's just take a look at the following NIST site:

https://www.physics.nist.gov/cuu/Units/introduction.html

This site covers all the most important aspects of units. In particular note how there are only seven basic units that all other units are build from. Why these seven? (no answer - set up a group chat to figure out why).

Before we continue further we should now start to use the "textbook" which is here on Libretexts (though any good review book can be used). So please read the following:

https://eng.libretexts.org/Sandboxes/bucky.prof/Introduction_to_Engineering/01%3A_Units (sandbox note: this link needs to be changed when this goes live...it will think it is email right now because of the @ symbol).

Ok now that we are done looking at that part of the textbook we can move on to the importance of keeping track of units.

Let us say a car is moving at 10 ⅔ meters per second (mps), how long does it take for it to go 5 ⅘ meters? Try this problem in class and discuss the answer.

The answer is 87 ⁄ 160 seconds (about a half of a second). Sometimes people with perfectly excellent math skills get this problem wrong. One of the most common answers to this question is 160 ⁄ 87 seconds (this is wrong!). Why is that? The simple answer, because people don't take the time to check their units. Generally they know what the unit should be but they don't check to see if their procedure will get that unit. Lets do a unit check. Let us first try each possible unit combination :$$\frac{meters}{seconds} + meters$$Ok this clearly can't be done, the units are not alike and there is no way to convert one to the other, so as suspected addition (and by association subtraction) is not the way to solve this. Ok we did the obvious, lets go to less obvious now. $$\frac{meter}{seconds} \times meters = \frac{meters^2}{seconds}$$Ok this also is not going to work. You probably suspected that, but did you check the units? Next division, but here we have two possibilities because division is not commutative (at least not until you make it multiplication). $$\frac{meters}{seconds} \div \frac{meters}{1} = \frac{\cancel{meters}}{seconds} \times \frac{1}{\cancel{meters}} = \frac{1}{seconds}$$Hmmm...looks kinda of right, but it is wrong. Dividing this way is the reason that 160 ⁄ 87 (the unit is "assumed" not checked) is one of the most common erroneous answers. Let's check the right way for completeness sake. $$\frac{meters}{1} \div \frac{meters}{seconds} = \frac{\cancel{meters}}{1} \times \frac{seconds}{\cancel{meters}} = {seconds}$$So now this gets us the right units and hence the right answer. Note this is a rather easy example (and can be done in your head), when problems get tougher (and can't be done in your head) this unit check can be used to help ensure you are getting the correct answer (sometimes it can even help you "remember" your formulas).