DA

A distilled, stet-by-step method for using dimensional analysis to convert units.

A common use of dimensional analysis is to provide a relatively foolproof method of determining whether to use multiplication or division to convert units. By following the rules of DA one can be sure this is always done correctly.
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Below are some step-by-step instructions:

1. Write down the number (and units) to be converted over 1.

Convert 28 inches to feet

28 in.
1

2. Determine the conversion factor
Example 12 inches = 1 ft

3. Write the conversion factor as a fraction such that the units on the top of your first fraction (inches in the example above) match the units on the bottom of the conversion fraction.
Example:

1 ft.
12 in.

4. Multiply the two fractions together, canceling out the original units.

28 in. x 1 ft. =
1     12 in.

28 ~~in.~~ x 1 ft. = ? ft.
1     12 ~~in.~~

28₌2.33 ft.
12

Note: The ultimate result of all this was the division problem:

28
12

If the problem had been to convert 28 feet to inches one would once again write the conversion factor as a fraction such that the units on the top of your first fraction (feet in the new example) match the units on the bottom of the conversion fraction.
Example:

28 ft. x 12 in. =
1      1 ft.

28 ft. x 12 in. =
1      1 ft.

28 x 12 = 336 inches

Note: The ultimate result of all this was a multiplication problem. Hence the statement at the beginning that DA is a technique to insure that one always makes the correct decision regarding multiplication or division.