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Convert the following measurement:

[tex]\[ 7.3 \times 10^{-6} \frac{ kg }{ mol \cdot dL } = \square \frac{ g }{ mol \cdot L } \][/tex]

Answer :

To convert the measurement [tex]\(7.3 \times 10^{-6} \frac{ kg }{ mol \cdot dL }\)[/tex] to [tex]\(\frac{ g }{ mol \cdot L }\)[/tex], follow these steps:

1. Understand the units and conversion factors:
- We need to convert kilograms (kg) to grams (g).
- We need to convert deciliters (dL) to liters (L).

2. Convert kg to g:
- We know that [tex]\(1 \text{ kg} = 1000 \text{ g}\)[/tex].
- Multiply the given value by the conversion factor for mass.
[tex]\[
7.3 \times 10^{-6} \text{ kg} \times 1000 \text{ g/kg} = 7.3 \times 10^{-3} \text{ g}
\][/tex]

3. Convert dL to L:
- We know that [tex]\(1 \text{ dL} = 0.1 \text{ L}\)[/tex].
- To convert from [tex]\(\frac{\text{unit}}{\text{dL}}\)[/tex] to [tex]\(\frac{\text{unit}}{\text{L}}\)[/tex], we need to divide the value by 0.1 (or equivalently, multiply by [tex]\(10)).
\[
7.3 \times 10^{-3} \frac{\text{g}}{\text{mol} \cdot \text{dL}} \times 10 = 7.3 \times 10^{-2} \frac{\text{g}}{\text{mol} \cdot \text{L}}
\]

4. Conclusion:
The final converted measurement is:
\[
0.073 \frac{g}{mol \cdot L}
\]

Thus, \(7.3 \times 10^{-6} \frac{kg}{mol \cdot dL} = 0.073 \frac{g}{mol \cdot L}\)[/tex].

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