To convert the given measurement from [tex]\( \frac{kg}{mol \cdot dL} \)[/tex] to [tex]\( \frac{g}{mol \cdot L} \)[/tex], we need to follow a series of steps involving unit conversions. Let's go through this step-by-step:
1. Express the given measurement with proper units:
[tex]\[
9.5 \times 10^{-4} \frac{kg}{mol \cdot dL}
\][/tex]
2. Convert kilograms (kg) to grams (g):
- We know that [tex]\( 1 \text{ kg} = 1000 \text{ g} \)[/tex].
- Therefore, the given value in grams per mole per deciliter is:
[tex]\[
9.5 \times 10^{-4} \frac{kg}{mol \cdot dL} \times 1000 \frac{g}{kg}
\][/tex]
- This simplifies to:
[tex]\[
9.5 \times 10^{-4} \times 1000 \frac{g}{mol \cdot dL} = 0.95 \frac{g}{mol \cdot dL}
\][/tex]
3. Convert deciliters (dL) to liters (L):
- We know that [tex]\( 1 \text{ dL} = 0.1 \text{ L} \)[/tex].
- Therefore, to convert [tex]\( \frac{g}{mol \cdot dL} \)[/tex] to [tex]\( \frac{g}{mol \cdot L} \)[/tex]:
[tex]\[
0.95 \frac{g}{mol \cdot dL} \times \frac{1}{0.1} \frac{dL}{L}
\][/tex]
- This simplifies to:
[tex]\[
0.95 \times 10 \frac{g}{mol \cdot L} = 9.5 \frac{g}{mol \cdot L}
\][/tex]
So, the converted measurement is:
[tex]\[
9.5 \frac{g}{mol \cdot L}
\][/tex]
Now, when taking into account the precision of the given value and the computation involved, the final result calculated is:
[tex]\[
\boxed{9.5}
\frac{g}{mol \cdot L}
\][/tex]
So,
[tex]\[
9.5 \times 10^{-4} \frac{kg}{mol \cdot dL} = 9.499999999999998 \frac{g}{mol \cdot L}
\][/tex]
Thus, the measurement after conversion is approximately [tex]\( 9.5 \frac{g}{mol \cdot L} \)[/tex].
