Answer:
About 0.566 L.
Explanation:
Let the substance be represented by X.
We want to determine how much volume in L will 8,326 dg (decigrams) of the substance which has a density of 1.47 g/mL occupy.
To convert from 8,326 dg to L, we can first convert from dg to g, g to mL using the density, and mL to L.
Recall that 1 g = 10 dg and 1 L = 1000 mL. We are also given that the density of X is 1.47 g/mL. This yields three ratios:
[tex]\displaystyle \frac{1 \text{ g X}}{10\text{ dg X}}, \, \frac{1 \text{ mL X}}{1.47 \text{ g X}}, \text{ and } \frac{1 \text{ L X}}{1000\text{ mL X}}[/tex]
Starting with the initial value, multiply:
[tex]\displaystyle 8326 \text{ dg X} \cdot \frac{1 \text{ g X}}{10 \text{ dg X}} \cdot \frac{1 \text{ mL X}}{1.47 \text{ g X}} \cdot \frac{1 \text{ L X}}{1000 \text{ mL X}} = 0.566 \text{ L X}[/tex]
Hence, 8,326 dg of the substance occupies about 0.566 L.
