Let's analyze each proposed multiplication or division of measurements step-by-step to decide whether each is possible and, if so, determine the result.
1. [tex]\(\frac{720 \, \text{mg}^2}{0.000 \, \text{g}}\)[/tex]
- Is this possible? Yes.
- Result: The division of any number by zero is mathematically undefined, which holds for units and measurements as well. Although it is often considered conceptually possible, it results in an undefined value.
- Answer: Undefined (division by zero).
2. [tex]\((1.0 \, \text{mL}) \cdot (7.0 \, \text{mL})\)[/tex]
- Is this possible? No.
- Result: Multiplying volumes (mL * mL) does not yield a meaningful physical quantity. It’s equivalent to finding the product of two separate volumetric measurements, which is nonsensical in most practical contexts.
- Answer: Not applicable.
3. [tex]\((3.0 \, \text{kg}) \cdot (1.0 \, \text{m}^3)\)[/tex]
- Is this possible? Yes.
- Result: Multiplying mass by volume is meaningful and results in a product with the physical units kg [tex]\(\cdot\)[/tex] m[tex]\(^3\)[/tex]. Here, [tex]\(3.0 \, \text{kg} \times 1.0 \, \text{m}^3 = 3.0 \, \text{kg} \cdot \text{m}^3\)[/tex].
- Answer: [tex]\(3.0 \, \text{kg} \cdot \text{m}^3\)[/tex].
So, the completed table is:
\begin{tabular}{|c|c|c|}
\hline \begin{tabular}{c}
proposed \\
multiplication or division
\end{tabular} & \begin{tabular}{c}
Is this \\
possible?
\end{tabular} & result \\
\hline
[tex]\(\frac{720 \, \text{mg}^2}{0.000 \, \text{g}} =\)[/tex] & Yes & Undefined (division by zero) \\
\hline
[tex]\((1.0 \, \text{mL}) \cdot (7.0 \, \text{mL}) =\)[/tex] & No & \\
\hline
[tex]\((3.0 \, \text{kg}) \cdot (1.0 \, \text{m}^3) =\)[/tex] & Yes & [tex]\(3.0 \, \text{kg} \cdot \text{m}^3\)[/tex] \\
\hline
\end{tabular}
