A fish maintains its depth in salt water adjusting the air content of your bone porous or its air pockets to make its density average is the same as that of the water. Suppose the fish has a density of 1.08 g/cm3 with its airbags crushed. What fraction of the volume of His expanded body must fish inflate the air bags to reduce its average density to of the water? Suppose the density of air is 0.00121 g/cm3.

1. Let's define:
- $\rho_{\text{fish}} = 1.08 \, \text{g/cm}^3$ (density of the fish with airbags crushed)
- $\rho_{\text{air}} = 0.00121 \, \text{g/cm}^3$ (density of air)
- $\rho_{\text{water}} = 1.025 \, \text{g/cm}^3$ (typical density of saltwater)

2. Use the formula for average density of the fish with inflated airbags:
\rho_{\text{average}} = \frac{V_{\text{fish}} \cdot \rho_{\text{fish}} + V_{\text{air}} \cdot \rho_{\text{air}}}{V_{\text{total}}},
where $V_{\text{fish}} + V_{\text{air}} = V_{\text{total}}$.

3. The condition is $\rho_{\text{average}} = \rho_{\text{water}}$.

4. Solve for the fraction of the volume of air, $\frac{V_{\text{air}}}{V_{\text{total}}}$:
\rho_{\text{water}} = \frac{V_{\text{fish}} \cdot \rho_{\text{fish}} + V_{\text{air}} \cdot \rho_{\text{air}}}{V_{\text{total}}},
V_{\text{air}} = V_{\text{total}} - V_{\text{fish}},
\rho_{\text{water}} = \frac{(V_{\text{total}} - V_{\text{air}}) \cdot \rho_{\text{fish}} + V_{\text{air}} \cdot \rho_{\text{air}}}{V_{\text{total}}},
\rho_{\text{water}} = \rho_{\text{fish}} - \frac{V_{\text{air}} \cdot \rho_{\text{fish}} - V_{\text{air}} \cdot \rho_{\text{air}}}{V_{\text{total}}},
V_{\text{air}} = V_{\text{total}} \cdot \frac{\rho_{\text{fish}} - \rho_{\text{water}}}{\rho_{\text{fish}} - \rho_{\text{air}}}.

5. The fraction is:
\frac{V_{\text{air}}}{V_{\text{total}}} = \frac{\rho_{\text{fish}} - \rho_{\text{water}}}{\rho_{\text{fish}} - \rho_{\text{air}}} = \frac{1.08 - 1.025}{1.08 - 0.00121}.

6. Calculate the fraction:
\frac{V_{\text{air}}}{V_{\text{total}}} \approx \frac{0.055}{1.07879} \approx 0.051.

7. The fish must inflate the air bags approximately:
5.1\% of its total volume to achieve the desired average density.