Questions: 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 proposed multiplication or division Is this possible? result (1.0 g^2) · (0.022 kg) =? - yes O no ■ 30 · g / 6.0 cm^2 =? - yes no (1) (7.0 g) · (4.0 g) =? - yes O no 28.0 g^2

Solution Steps

The first proposed operation is \((1.0 \, \text{g}^2) \cdot (0.022 \, \text{kg})\). To determine if this multiplication is possible, we need to consider the units involved. The units are \(\text{g}^2\) and \(\text{kg}\). Multiplying these units is possible, resulting in \(\text{g}^2 \cdot \text{kg}\).

The numerical calculation is straightforward: \[ 1.0 \times 0.022 = 0.022 \] Thus, the result of the multiplication is \(0.022 \, \text{g}^2 \cdot \text{kg}\).

The second proposed operation is \(\frac{30 \, \text{g}}{6.0 \, \text{cm}^2}\). Division of these units is possible, resulting in \(\text{g/cm}^2\).

Perform the division: \[ \frac{30}{6.0} = 5.0 \] Thus, the result is \(5.0 \, \text{g/cm}^2\).

The third proposed operation is \((7.0 \, \text{g}) \cdot (4.0 \, \text{g})\). Multiplying these units is possible, resulting in \(\text{g}^2\).

The result is already provided as \(28.0 \, \text{g}^2\), which is correct since: \[ 7.0 \times 4.0 = 28.0 \]

Final Answer