Introduction to dimensional analysis, or how to use ratios to convert measurement units

We can convert any measuring unit to another by multiplying it by a very special ratio (or ratios) that equals ONE. We can form these special ratios from the conversion factors. For example, 1 ft = 12 in is a conversion factor, and we can write from it the ratios 1 ft/12 in and 12 in/1 ft, which both equal 1.

Then, to convert a measurement in inches into feet, we can multiply it by the ratio 1 ft/12 in. The inches will cancel out as units, and we get a result that is in feet.

This is a very useful technique when the conversions are more complex, such as converting between metric and customary systems. Often, you need to use several ratios in a "chain" — called "chaining", which is explained in the 2nd part of this lesson (below).

This introductory lesson is meant for 6th grade and onward.

In this 2nd video we take a look at CHAINING when using ratios to convert measurement units (dimensional analysis). It simply means using two or more of those ratios that we make from the conversion factors, in order to convert one measurement to another. This technique is especially often necessary in science, or when converting between the customary and the metric measuring systems.

See also

Word problems involving unit rates

Math Mammoth Grade 6 curriculum

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