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How do I use the picket fence method?

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2 Answers

Hi Jensen,
 
The best way to think about units is as if they were variables in an algebra equation.  For example, if you had the variable "a" on the top and bottom of a fraction you would eliminate it because it cancels itself out.  The same thing can be said for units.  The picket fence outlined in your example is just a way of helping you set up your math problem so that you have units on top and bottom that ultimately cancel out.  The "conversion factors" being used can be anything where what's on the top and bottom are equal.  In other words, 1 km and 1000 m are the same thing, 2.54 cm and 1 in are the same thing, so on and so on.  If then you wanted to know how many centimeters in a foot you would start with 1 ft then multiply it by (12in/1ft) because the "ft" on top and bottom would cancel (leaving you with inches).  Then you would do the same thing with (2.54cm/1in), leaving you with centimeters.  If you do the process in multiple steps it makes a little more sense.  The picket fence method just allows you to string a bunch of conversation factors together in order to speed things up.
 
Hope this helps!
How many kilometers in a mile?
 
We know:
2.54 centimeters = 1 inch (exactly)
12 inches = 1 foot (exactly)
5280 feet = 1 mile (exactly)
1 kilometer = 1000 meters (exactly)
1 meter = 100 centimeters (exactly)
 
Now you draw a "picket fence":
 
|        |         |         |
---------------------------
|        |         |         |
 
Then you fill it with appropriate conversion factors based on units.
 
The first unit in top left and the last unit in the bottom right should be the units you're looking for.
 
| 1 km | . . . | . . . . |
--------------------------------
| . . . . | . . . | . . . . | 1 mile
 
Between every two pickets should be a valid conversion factor.
 
| 1 km . . | 1 m . . .| 2.54 cm | 12 in | 5280 ft |
-----------------------------------------------------------
| 1000 m | 100 cm | 1 in . . . .| 1 ft . | 1 mi . .|
 
The unit in the top between two pickets should be the same as the unit in the bottom of the pickets to the left.
 
When you're done you've got a fraction with factors in the numerator and factors in the denominator; evaluate it. Note how all the units cancel (treat them as numbers) except the ones you want.
 
The picket fence above results in:
1.609344 km / mi (exactly)