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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.

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