If average depth of an ocean is $$4000$$ m and the bulk modulus of water is $$2 \times 10^9 \text{ N m}^{-2}$$, then fractional compression $$\frac{\Delta V}{V}$$ of water at the bottom of ocean is $$\alpha \times 10^{-2}$$. The value of $$\alpha$$ is _______, (Given, $$g = 10 \text{ m s}^{-2}, \rho = 1000 \text{ kg m}^{-3}$$)

The fractional compression is given by:

$$\frac{\Delta V}{V} = \frac{P}{B}$$

where $$P$$ is the pressure at the bottom and $$B$$ is the bulk modulus.

Pressure at the bottom: $$P = \rho g h = 1000 \times 10 \times 4000 = 4 \times 10^7$$ N/m$$^2$$

$$\frac{\Delta V}{V} = \frac{4 \times 10^7}{2 \times 10^9} = 2 \times 10^{-2}$$

So $$\alpha = 2$$.

The answer is $$\boxed{2}$$.