Conversions
Converting a rate from one set of units to another is a common maneuver in mathematics. We start with a
rate, which is any number expressed in a ratio of units. Examples of rates would be:
50 ,
100
,
25
,
12
, etc.
Suppose we want to convert 50 miles per hour into feet per second. (The “per” is the division line). We
would use the following conversions:
1 mile = 5,280 feet
1 hour = 60 minutes
1 minute = 60 seconds
The conversion can be done all in one big step by setting up conversion ratios, such that you systematically
cancel out units until you are left with the desired units. Thus, to convert 50 miles per hour into feet per
second, we would do the following:
(
)* + ,∙(
),./* + + + )*×),./* , ∙ (0* , ∙ (0* , = 0*×0*
= 73.333 .
You can see how the units cancel, but the numbers stay behind:
Another example: Suppose your car gets 25 miles per gallon of gas. How many kilometers would it get per
liter of gas?
Answer: you may need to look up some conversion formulas. I found a pretty good table at this website:
http://www.fhwa.dot.gov/publications/convtabl.cfm. We need the following conversions:
1 mile = 1.61 kilometers
1 gallon = 3.785 liters
So we set up a series of ratios to be multiplied out, with units cancelling:
.) + ( + , ∙ (8.9/) , ∙ (
+.0+ :
+ ,=
.)×+.0+ :
8.9/) = 10.634
:
.
Here’s one for you to try: Gold costs $850 per ounce. What would the equivalent cost be in Canadian dollars
per gram? Assume that $1 (US) = $0.96 (Canadian). You should get (CDN)$28.78 per gram. See if you can set
up the set of ratios and replicate my result.