A Foolproof Method of Unit Conversion

Unit Converter

Unit conversion is not always so simple as moving the decimal place. The following example gives 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.

 

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