Determine the estimated change in the density of water in the ocean...

The change in pressure at a depth $h$ is given by:

$\Delta P = \rho g h$

The bulk modulus $B$ relates the change in pressure to the fractional change in density:

$B = \dfrac{\Delta P}{\dfrac{\Delta \rho}{\rho}}$

Rearranging for the change in density $\Delta \rho$:

$\Delta \rho = \dfrac{\rho \Delta P}{B} = \dfrac{\rho^2 g h}{B}$

Substituting the given values (using $g = 9.8 \text{ m/s}^2$):

$\Delta \rho = \dfrac{(1030)^2 \times 9.8 \times 400}{2 \times 10^9}$

$\Delta \rho = \dfrac{1060900 \times 3920}{2 \times 10^9}$

$\Delta \rho = \dfrac{4.158 \times 10^9}{2 \times 10^9}$

$\Delta \rho \approx 2.08 \text{ kg/m}^3$

Rounding to the nearest integer, the estimated change in density is $2 \text{ kg/m}^3$.