Flashcard 9 - Mathematics Flashcard Set for the HESI Exam

The method used is called dimensional analysis, also known as the conversion factor method. It involves expressing the numbers and dimensions of a thing in one unit of measurement in terms of another without changing the value of that thing. This requires canceling out unnecessary units while solving equations.

This method is useful for performing unit conversions, especially complex unit conversions (such as converting from the English System to the International or metric system).

Here is an example:

Convert \(23\) days to seconds.

\[\require{cancel} 23\,\cancel{\text{days}} \cdot \frac{(24\,\cancel{\text{hours}})}{(1\,\cancel{\text{day}})} \cdot \frac{(60\,\cancel{\text{minutes}})}{(1\,\cancel{\text{hour}})} \cdot \frac{(60\,\text{seconds})}{(1\,\cancel{\text{minute}})} = 1987200\,\text{seconds}\]

Notice that a measurement unit occurring on top of a fraction cancels out the same unit at the bottom of the fraction. All other units are canceled in this manner, leaving only the desired unit.