Table of Contents |
Unit conversion is a simple process to overlook, but doing so can have dramatic effects on the results of any project we may be working on. For example, suppose someone told us that a machine needs to be able to handle a 50,000 N load. If we were in a country that uses the metric system, that may make perfect sense to us. If we are in the United States, where English units are used, that may not make any sense at all. The need then arises to convert 50,000 N into pounds (lbs.), so that we can more easily understand the quantities we are working with. Unit conversion allows us to express 50,000 N as roughly 11,240 lbs.,or 5.62 tons. While the numbers and units are different, the actual quantity they represent is the same.
Lets look at how to do some unit conversion.
In order to convert units, we first need to understand something called a conversion factor, which is basically a fraction equaling 1 that relates two different units.
EXAMPLE
Suppose we have 160 cups of water, and we want to determine how many gallons of water this is equal to. Before we make any calculations, we might recall that there are 16 cups in one gallon of water. This knowledge will help us determine what our conversion factor will be.Conversion factor: 1 gallon = 16 cups | |
Multiplying across numerators and denominators | |
Units of cups cancel | |
Our Solution |
In the above example of converting seconds to hours, suppose we did not know a conversion factor between hours and seconds. Do you think we can make the conversion?
Of course! In cases such as this, we may wish to use multiple conversion factors to help us make a conversion. For example, we may know that there are 60 seconds in 1 minute, and 60 minutes in 1 hour.
Therefore, we can do the following:
EXAMPLE
Conversion factors: 1 min = 60 sec; 1 hr = 60 min | |
Multiply numerators and denominators | |
Units of seconds and minutes cancel, leaving hours | |
Our Solution |
Sometimes when converting units, we may need to convert between squared units (area) or cubed units (volume). In these instances, we follow the same process as before, but we have to be careful with our conversion factors. Let's look at some examples.
EXAMPLE
Suppose we are told that we need to convert 200 square feet into square inches. How would we go about doing this calculation?Conversion factor: 1 sq ft = 144 sq in | |
Multiply numerators and denominators | |
Units of square feet cancel, leaving square inches | |
Our Solution |
EXAMPLE
Suppose you want to convert 5 cubic feet to liters. How would you make this conversion given that there are approximately 30.48 centimeters in 1 foot and 0.001 liters in 1 cubic centimeter?Conversion factors factors for to and to L | |
Multiply numerators and denominators | |
Units of and cancel, leaving L | |
Our Solution, rounded to the hundredths place |
Source: ADAPTED FROM "BEGINNING AND INTERMEDIATE ALGEBRA" BY TYLER WALLACE, AN OPEN SOURCE TEXTBOOK AVAILABLE AT www.wallace.ccfaculty.org/book/book.html. License: Creative Commons Attribution 3.0 Unported License