Questions: Measurement and Matter Multiplication and division of measurements Decide whether each proposed multiplication or division of m proposed multiplication or division Is this possible? result --------- (9.0 g^3) ⋅ (5.0 g^2)=? yes no (1.0 mg) ⋅ (0.032 g)=? yes (3.3 cm) ⋅ (0.10 m)=? no Just output the content of the question, DO NOT output additional information or explanations.

Measurement and Matter Multiplication and division of measurements Decide whether each proposed multiplication or division of m proposed multiplication or division Is this possible? result --------- (9.0 g^3) ⋅ (5.0 g^2)=? yes no (1.0 mg) ⋅ (0.032 g)=? yes (3.3 cm) ⋅ (0.10 m)=? no Just output the content of the question, DO NOT output additional information or explanations.
Transcript text: Measurement and Matter Multiplication and division of measurements Decide whether each proposed multiplication or division of $m$ \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$\left(9.0 \mathrm{~g}^{3}\right) \cdot\left(5.0 \mathrm{~g}^{2}\right)=?$ & \begin{tabular}{c} yes \\ no \end{tabular} & $\square$ \\ \hline$(1.0 \mathrm{mg}) \cdot(0.032 \mathrm{~g})=?$ & $\square$ yes & $\square$ \\ \hline$(3.3 \mathrm{~cm}) \cdot(0.10 \mathrm{~m})=?$ & no & $\square$ \\ \hline \end{tabular}
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Solution

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Solution Steps

Step 1: Verify Unit Compatibility and Physical Feasibility

Since we are multiplying, we combine the units. The operation is physically meaningful.

Step 2: Perform Operation

The operation performed is multiplication.

Step 3: Apply Unit Arithmetic

For multiplication, units are combined and their exponents added. The resulting unit is (g^3 * g^2).

Final Answer:

The result of the operation is 45 (g^3 * g^2).

Step 1: Verify Unit Compatibility and Physical Feasibility

Since we are multiplying, we combine the units. The operation is physically meaningful.

Step 2: Perform Operation

The operation performed is multiplication.

Step 3: Apply Unit Arithmetic

For multiplication, units are combined and their exponents added. The resulting unit is (mg^1 * g^1).

Final Answer:

The result of the operation is 0.032 (mg^1 * g^1).

Step 1: Verify Unit Compatibility and Physical Feasibility

Since we are multiplying, we combine the units. The operation is physically meaningful.

Step 2: Perform Operation

The operation performed is multiplication.

Step 3: Apply Unit Arithmetic

For multiplication, units are combined and their exponents added. The resulting unit is (cm^1 * m^1).

Final Answer:

The result of the operation is 0.33 (cm^1 * m^1).

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