Unformatted text preview: raically. In the final
analysis, all we really need to do is make sure that the units all cancel such that the units
of the final answer match the units we seek. All we really need to do is make sure that the units all cancel such that the
units of the final answer match the units we seek!
I felt that that needed reiteration. It's the heart of the factor label method, however, so it
warrants this reiteration.
To be sure that the units cancel, there are a few simple points to keep in mind.
ALWAYS use consistent units! (For instance, feet and cm are length units, but
feet don't cancel out cm!!) Dakota State University page 220 of 232 Factor Label Method General Chemistry I and II Lab Manual (2)
ALWAYS write the units down AVOIDING superfluous units (made up units
that don't belong)!!
ALWAYS be sure that the units cancel out by having one in the denominator and
the other in the numerator or vice versa.
ALWAYS be sure the units of the final answer match the units you are seeking.
Beware, however, of one point. The factor label method will tell you if an answer is
wrong if the units are not the units you want. However, if a unitless number is needed
(such as π ), then the units will match, but the answer will still be wrong.
A few examples:
Example 1: Recently, I have been putting together an electric race car track (remember
the electric slot cars? No? Am I showing my age?). The track occupies what would be
my bedroom were I married, but since I'm a bachelor, it is more important to me to have
an electric race car track than a bed. Anyway, I have 120 track pieces, an average of 9
inches each, on a scale of 1:87. What is the scale length of my track in miles?
GIVEN: 120 track pieces, 9 inches/piece, scale 1:87
FIND: miles of scale track
CONVERSION FACTORS: We will find we need 12 in/ft, and 5,280 ft/mile. In
a problem, you typically will not know what conversion factors you will need ahead of
time, but as you perform the problem, you will see how they are required. For instance,
if you know the conversion factor 5,280 ft/mile, and you are at "inches" in the problem,
then you will know you need to convert from inches to feet, or 12 in/ft.
Let's set it up and see what we get:
120 piece * 9inch 87inch
piece inch 12inch 5,280 foot Notice how all units cancel, piece with piece, inch by inch, foot cancels foot. The term
"87 inch / 1 inch" is our scale factor. By convention, scale factors have really no units. I
just included "inch" terms to make it easier to see how I got that term, but even so, the
inches in this conversion factor would cancel with themselves, making the scaling factor
unitless. You may also notice that the "grammar" is not quite correct, since foot is
singular but there are 5,280 of them. However, using "feet" rather than "foot" can lead to
confusion as to whether or not a unit can cancel, so I always just use singular units and
try to avoid plurals.
Example 2: Some calculations are made much easier by not requiring the memorization
of some formula, which sometimes means you can...
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