Let's break down and solve the problem.

We are given:

• The mass of the gemstone: $m = 3.2 \, \text{grams}$
• The volume of water displaced by the gemstone: $V = 0.16 \, \text{liters}$

Step 1: Convert the volume from liters to cubic centimeters (cm³)

We know that: $1 \, \text{liter} = 1000 \, \text{cm}^3$ So, $V = 0.16 \, \text{liters} = 0.16 \times 1000 = 160 \, \text{cm}^3$

Step 2: Use the density formula

The formula for density $\rho$ is: $\rho = \frac{m}{V}$ Substitute the known values: $\rho = \frac{3.2 \, \text{g}}{160 \, \text{cm}^3} = 0.02 \, \text{g/cm}^3$

Answer:

The density of the gemstone is $0.02 \, \text{g/cm}^3$.

Would you like further details on any of the steps? Here are a few related questions you might consider:

1. How does the displacement method relate to Archimedes' principle?
2. Why is it necessary to convert liters to cubic centimeters in this context?
3. How would the density calculation change if the gemstone displaced more or less water?
4. What are some common materials with densities similar to $0.02 \, \text{g/cm}^3$?
5. Could you express this density in different units, such as kg/m³?

Tip:

Always ensure unit consistency in density calculations, as volume can be in different units (liters, cm³, m³, etc.).