1 Units
Suppose you ask me “How far is the closest grocery store?” and I answered “3”.
You would justifiably be pissed off: 3 what? 3 blocks? 3 miles? To give a complete answer, you must specify the units you are using to measure distance. In this case, the question demanded that my answer specify units of length, e.g. meters, miles, blocks, or any other such unit. Your answer must include the units used in the measurement! The same is true for units of time. If I ask you how long before the movie starts, and you reply “5”, I have no idea if that means 5 seconds, 5 minutes, or something else entirely.
When reporting a physical quantity, you must always specify the units used.
The three basic type of units we will use in this class are length, time, and mass. For the most part, we will follow the International System of Units (or SI, for Système International), which measures length in meters (m), time in seconds (s), and mass in kilograms (kg). Note each unit has an abbreviation (e.g. “m” for meters, or “kg” for kilograms). These are standard, so I assume you’re familiar with them. If you run into an abbreviation you haven’t seen before, just google it.
This early emphasis on units is not gratuitous. As proof, I offer this example: in 1983, an Air Canada plane ran out of fuel at an altitude of 12,000 m (41,000 ft). Prior to take off, the ground crew used printed tables to figure out how much fuel the plane needed. The tables were in kilograms, but the ground crew measured the fuel in pounds. Since 
, the plane had roughly half the amount of fuel needed to complete the journey! Fortunately, the pilots were able to glide the plane to safety, and no serious injuries were reported. You can check out this wikipedia article for more details.
One thing you may need to do from time to time is change units. Say you want to know how many km is 2 million inches. The simplest way to do so is by using google: type “2*10^6 inches in km”, and the answer will pop right up (the “^” symbol mean exponentiation, so 10^6 stands for 
). In the rare occasion that google can’t help you (it does happen!), you may need to do this by hand. If so, the best way to do so is to use the “multiply by 1” method. Let’s see how this works with an example.
Example: Unit Conversion
Use the “multiply by 1” method to calculate how many km is 2 million inches.
You should now try your hand at doing this yourself.
Exercise 1.1: Unit Conversion
Use the “multiply by 1” method to find:
- how many seconds are there in 2 days.
- how many ounces in 12 liters (3.8 liters = 1 gallon, 1 gallon = 8 pints, and 1 pint = 16 oz.)
Obviously I’m not asking you to type this into google: you really do need to know how to convert units by hand! While rare, google will sometimes throw up its hands at you.
If you struggled with this problem, you can see the solution to the first question below.
If you had to look up the solution, there are some more practice problems below. Make sure you are comfortable with how unit conversion works.
Key Takeaways
Practice Problems (PP):
PP 1.1: How many minutes in 3 decades? If you get stuck, you can see the solution below.
PP 1.2: How many mL in 5 quarts? Some useful conversions: 
, and 
.