Question

dimensional analysis utilizes ______ to solve unit conversion problems.
○ fraction multiplication
○ conversion factors
○ unit cancellation
○ all of the above

Explanation:

• Fraction multiplication: In dimensional analysis, we multiply fractions (conversion factors as fractions) to convert units. For example, to convert meters to centimeters, we use the conversion factor $\frac{100\ \text{cm}}{1\ \text{m}}$ and multiply by the original quantity.
• Conversion factors: These are essential in dimensional analysis. A conversion factor is a ratio of equivalent quantities (e.g., $1\ \text{kg} = 1000\ \text{g}$, so the conversion factor can be $\frac{1\ \text{kg}}{1000\ \text{g}}$ or $\frac{1000\ \text{g}}{1\ \text{kg}}$) that is used to change the units of a measurement.
• Unit cancellation: Also known as dimensional analysis or factor - label method, we cancel out units that appear in both the numerator and denominator. For example, if we have $5\ \text{m}$ and we want to convert to centimeters, we use $\frac{100\ \text{cm}}{1\ \text{m}}$, and the "m" units cancel out: $5\ \text{m}\times\frac{100\ \text{cm}}{1\ \text{m}} = 500\ \text{cm}$. Since all three (fraction multiplication, conversion factors, and unit cancellation) are used in dimensional analysis for unit conversion, the correct option is "All of the above".

Answer:

D. All of the above