If average depth of an ocean is 4000m and the bulk modulus of water...

The formula to calculate the Bulk modulus is given by

$B = - \dfrac{∆ P}{\left(\dfrac{∆ V}{V}\right)} . . . \left(1\right)$

From equation (1), the fractional compression in volume may be obtained as follows:

$\begin{cases}- \left(\dfrac{\DeltaV}{V}\right) & = & \dfrac{∆ P}{B} \\ & = & \dfrac{ρg ∆ h}{B} . . . \left(2\right)\end{cases}$

From equation (2) it follows that

$\begin{cases}\left|- \left(\dfrac{∆ V}{V}\right)\right| & = & \dfrac{1000 \times 10 \times 4000}{2 \times {10}^{9}} \\ & ⇒ & \left(\dfrac{∆ V}{V}\right) = 2 \times {10}^{- 2}\end{cases}$

Hence, $\alpha = 2$.