Question

How much volume (in L) will 8,326 dg of a substance having a density of 1.47 g/mL occupy?

Answer 1

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:

$\displaystyle \frac{1 \text{ g X}}{10\text{ dg X}}, \, \frac{1 \text{ mL X}}{1.47 \text{ g X}}, \text{ and } \frac{1 \text{ L X}}{1000\text{ mL X}}$

Starting with the initial value, multiply:

$\displaystyle 8326 \text{ dg X} \cdot \frac{1 \text{ g X}}{10 \text{ dg X}} \cdot \frac{1 \text{ mL X}}{1.47 \text{ g X}} \cdot \frac{1 \text{ L X}}{1000 \text{ mL X}} = 0.566 \text{ L X}$

Hence, 8,326 dg of the substance occupies about 0.566 L.