Final answer:
Ratios compare quantities of the same kind, so 5 grams and 16 millimeters cannot form a ratio. Unit conversion within the same measurement system is done via unit analysis, using known ratios to convert to the desired units. Selecting the right unit makes numbers easier to manage.
Step-by-step explanation:
In mathematics, ratios are a way to compare two quantities. To express 5 grams and 16 millimeters as a ratio, both quantities must be of the same kind, such as length to length or mass to mass. Since grams measure mass and millimeters measure length, they are not comparable and cannot form a ratio. However, converting units within the same measurement system, such as between metric units, is possible using unit conversion.
For instance, to convert from milligrams to nanograms, you multiply by the appropriate conversion factors. This process is known as unit analysis or dimensional analysis, and it involves multiplying the given measurement by a known ratio that has the desired unit, which cancels out the initial unit, resulting in the conversion. An example is converting 0.0034 grams to milligrams by using the known ratio of 1 mg to 10-3 grams.
For practical purposes, it's often helpful to use units that result in smaller, more easily managed numbers. Therefore, you should choose the most appropriate unit that makes the numerical value comfortable to work with, especially when dealing with either very small or very large quantities. Selecting the right unit can help in clarity and ease of use within a given context.