A Foolproof Method of Unit Conversion

Unit Converter

Unit conversion is not always so simple as moving the decimal place. The following examples give you a foolproof way to convert any quantity from one set of units to another when you know the conversion factors. Essentially, what you want to do is to set up the problem so that you can cancel all units except the ones that should be in the final answer. In complex problems, it is sometimes best to do this in a series of steps. You do it by multiplying your original value by the conversion factor. You flip the conversion factors so that the units you want to cancel will be both in the numerator and the denominator. What's left over is the answer you want.

Units: Units are important. You always need to include units when doing your calculations and reporting your answers. Here's a simple problem involving unit conversion. How many total hours of vacation do you need to claim if you work 8 hours per day and will be on vacation for 7 days? Your conversion factor is that there are 8 hours in 1 work day. You might see this written as 8 hours/day, but the 1 is assumed. This becomes more important in the second version of the problem.

8 hours/1 day * 7 days = 56 hours

Note that in this problem that the unit "days" is found on both the top (numerator) and bottom (denominator). When multiplying, those units cancel out, leaving the answer in hours. See how this is a check on whether you set up the problem right? If the units don't cancel, leaving you only with the correct ones, you did something wrong. The rest is just math for the calculator, but setting up the problem right requires you to use your brain!

Now let's take that same example and reverse it. Imagine that you recorded 56 hours of work, but your employer needs you to report the vacation time in days. With a conversion factor, such as 8 hours = 1 work day, you can arrange it with either value on top. How you do it depends on what units you want to remain in your answer, and which units you want to cancel out. If you want hours to cancel, leaving you an answer in days, you put days on top and hours on the bottom of the conversion factor.

1 day/8 hours * 56 hours = 7 days

Here's a challenging problem involving unit conversion: Convert the speed of light from meters per second to miles per hour.

Given information:

C=speed of light = 2.998 x 108 m/sec

Given conversion factors:

 100 cm = 1 m 60 sec = 1 min 2.54 cm = 1 inch 60 min = 1 hr 12 inches = 1 ft 5280 ft = 1 mile

The trick to this problem is to break it down into easier to manage pieces, since it actually involves two conversions (distance units and time units).

Step 1: Convert time units from meters per second to meters per hour. Since there are 60 seconds per minute, and 60 minutes per hour, multiply meters per second by seconds per minute and minutes per hour to get your answer. Note that seconds and minutes cancel since they are in both the numerator and the denominator.

(2.998 x 108 m/sec) x (60 sec/min) x (60 min/hr) = 1.07928x1012 m/hr

Step 2: Convert Metric System units from meters to centimeters using the given conversion factor. Why centimeters? Because you haven't been given the conversion factor to go directly from meters to miles. You only know how to convert meters to centimeters, centimeters to inches, inches to feet and feet to miles.

(1.07928 x 1012 m/hr) x (100 cm/m) = 1.07928x1014 cm/hr

Step 3: Convert English System units from inches to miles using the given information.

(1.07928x1014 cm/hr) x (1 in/2.54 cm) x (1 ft/12 in) x (1 mi/5280 ft) = 670,633,500.4 mi/hr