Which of the following best describes how dimensional analysis is used to convert units of measure?

• A. By dividing the original value by the sum of all conversion factors.
• B. By replacing the original units with the desired units without using conversion factors.
• C. By multiplying the original value by conversion factors that cancel out the unwanted units and introduce the desired units.
• D. By adding conversion factors to the original value until the desired unit is reached.

Answer: (C)

Verified step by step guidance

1. Understand that dimensional analysis is a method used to convert one unit of measurement to another by using conversion factors.
2. Recognize that a conversion factor is a ratio that expresses how many of one unit equals another unit, for example, \(\frac{1\ \text{inch}}{2.54\ \text{cm}}\) or \(\frac{2.54\ \text{cm}}{1\ \text{inch}}\).
3. Set up the problem by writing the original value multiplied by one or more conversion factors arranged so that the units you want to cancel appear diagonally opposite and cancel out.
4. Multiply the original value by the conversion factors, ensuring that the unwanted units cancel out and the desired units remain.
5. Calculate the numerical value after the units have been converted, confirming that the final answer has the correct units.