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Decide whether each proposed multiplication or division of measurements is possible. If it is possible, write the result in the last column of the table.

\begin{tabular}{|c|c|c|}
\hline
Proposed Multiplication or Division & Is this Possible? & Result \\
\hline
[tex]$(3.1 \, \text{dL}) \cdot (0.30 \, \text{L}) =$[/tex] ? &
\begin{tabular}{c}
Yes \\
No
\end{tabular} & [tex]$\square$[/tex] \\
\hline
[tex]$\left(3.0 \, \text{g}^3\right) \cdot (0.013 \, \text{kg}) =$[/tex] ? &
\begin{tabular}{l}
Yes \\
No
\end{tabular} & [tex]$\square$[/tex] \\
\hline
[tex]$(9.0 \, \text{mL}) \cdot (6.0 \, \text{mL}) =$[/tex] ? &
\begin{tabular}{l}
Yes \\
No
\end{tabular} & [tex]$\square$[/tex] \\
\hline
\end{tabular}


Sagot :

Let's carefully analyze each proposed multiplication and determine if it's possible, then we'll calculate the result if it's feasible.

### First proposed multiplication: [tex]\((3.1 \, \text{dL}) \cdot (0.30 \, \text{L})\)[/tex]

For this calculation, remember that 1 liter (L) is equal to 10 deciliters (dL). To perform the multiplication, we need to consider the unit conversion:
[tex]\[ 3.1 \, \text{dL} \times 0.30 \, \text{L} \][/tex]
[tex]\[ = 3.1 \, \text{dL} \times 0.30 \times 10 \, \text{dL} \quad \text{(since 1 L = 10 dL)} \][/tex]
[tex]\[ = 3.1 \times 3.0 \, \text{dL}^2 \][/tex]
[tex]\[ = 9.3 \, \text{dL}^2 \][/tex]

So, the multiplication is possible, and the result is [tex]\(0.93 \, \text{dL}^2\)[/tex].

### Second proposed multiplication: [tex]\((3.0 \, \text{g}^3) \cdot (0.013 \, \text{kg})\)[/tex]

In this case, we are trying to multiply units of different dimensions: cubic grams ([tex]\(\text{g}^3\)[/tex]) and kilograms (kg). These units are not compatible for multiplication in a meaningful physical context. Therefore, this multiplication is not possible, and no result needs to be calculated.

### Third proposed multiplication: [tex]\((9.0 \, \text{mL}) \cdot (6.0 \, \text{mL})\)[/tex]

Here we are trying to multiply two volumes, both in milliliters (mL). Multiplying two volumes together would result in a new unit of [tex]\(\text{mL}^2\)[/tex], which is not a standard or meaningful unit of measure for volume. Therefore, this multiplication is not considered possible in practical terms.

### Conclusion

Based on this analysis, we can fill in the table as follows:

[tex]\[ \begin{array}{|c|c|c|} \hline \text{proposed multiplication or division} & \text{Is this possible?} & \text{result} \\ \hline (3.1 \, \text{dL}) \cdot (0.30 \, \text{L}) & \text{yes} & 0.93 \, \text{dL}^2 \\ \hline \left(3.0 \, \text{g}^3\right) \cdot (0.013 \, \text{kg}) & \text{no} & \\ \hline (9.0 \, \text{mL}) \cdot (6.0 \, \text{mL}) & \text{no} & \\ \hline \end{array} \][/tex]
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