Question

use dimensional analysis to convert. how many grams are in 46 kilograms? (1 kg = 1000 g) which expression correctly shows the measurement multiplied by the conversion factor? \\(\frac{1}{46\\,\text{kg}} \cdot \frac{1\\,\text{kg}}{1000\\,\text{g}}\\) \\(\frac{1}{46\\,\text{kg}} \cdot \frac{1000\\,\text{g}}{1\\,\text{kg}}\\) \\(\frac{46\\,\text{kg}}{1} \cdot \frac{1\\,\text{kg}}{1000\\,\text{g}}\\) \\(\frac{46\\,\text{kg}}{1} \cdot \frac{1000\\,\text{g}}{1\\,\text{kg}}\\)

Explanation:

Step1: Identify starting measurement

We begin with the given value: $46\ \text{kg}$ (written as $\frac{46\ \text{kg}}{1}$ for dimensional analysis).

Step2: Select correct conversion factor

To cancel kg and get grams, use $\frac{1000\ \text{g}}{1\ \text{kg}}$ (since $1\ \text{kg}=1000\ \text{g}$).

Step3: Match to the correct expression

Multiply the starting measurement by the conversion factor: $\frac{46\ \text{kg}}{1} \cdot \frac{1000\ \text{g}}{1\ \text{kg}}$

Answer:

$\frac{46\ \text{kg}}{1} \cdot \frac{1000\ \text{g}}{1\ \text{kg}}$