When one moves from a point 16 km below the earth's surface to a...

The acceleration due to gravity at a depth $d$ below the earth's surface is given by:

$g_d = g\left(1 - \dfrac{d}{R}\right)$

The acceleration due to gravity at a height $h$ above the earth's surface (for $h \ll R$) is given by:

$g_h = g\left(1 - \dfrac{2h}{R}\right)$

Given $d = 16$ km and $h = 16$ km, we can find the values of $g_d$ and $g_h$:

$g_d = g\left(1 - \dfrac{16}{6400}\right) = g\left(1 - \dfrac{1}{400}\right)$

$g_h = g\left(1 - \dfrac{2 \times 16}{6400}\right) = g\left(1 - \dfrac{2}{400}\right)$

The magnitude of the change in acceleration due to gravity when moving from the depth $d$ to the height $h$ is:

$\Delta g = g_d - g_h = g\left(1 - \dfrac{1}{400}\right) - g\left(1 - \dfrac{2}{400}\right)$

$\Delta g = g\left(\dfrac{2}{400} - \dfrac{1}{400}\right) = \dfrac{g}{400}$

The percentage change in $g$ is approximately:

$\dfrac{\Delta g}{g} \times 100 = \dfrac{\dfrac{g}{400}}{g} \times 100 = \dfrac{100}{400} = 0.25\%$

Thus, the value of $\alpha$ is $0.25$.

Answer: $0.25$