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Using Units (Dimensional Analysis)

In working out calculations, units can provide an excellent source of
self-correction. When you perform a calculation in any science, you
will almsot always be looking not just for a number, but for a number of
a specific type of unit. If the answer your work yields does not have the
correct units, then you know you have made a mistake somewhere.

For instance, lets say that a person who weighs 150 lbs (a British
system measurement) wants to know her weight in kilograms (a metric
system measurement). Start by drawing a horizontal line, and then
making vertical hash marks to form a table as in step one of the figure
below.

Figure %: Units in calculations

The woman knows her weight in pounds and wants to find out what she weighs in
kilograms. As seen
in step two, she should enter the known weight in pounds next to the ratio of
pounds to kilograms (1 : 2.205) in
such a way that the units cancel one another. This means that if lbs are on
top, then there must be lbs on the
bottom, so that when they are divided, they cancel. Next, while carrying out
the obvious mathematical operation,
cancel the units. If the woman had accidentally put the ratio of pounds to
kilograms in upside
down (2.205 : 1), then the units would not have canceled out, alerting the woman
that she had made a mistake.