Answer
At a distance of 13,800 km above the earth's surface, the acceleration due to gravity is $0.98~m/s^2$.
Work Step by Step
Let $M$ be the mass of the earth.
Let $R$ be the radius of the earth.
(equation 1): $\frac{G~M}{R^2} = 9.80~m/s^2$
Let $h$ be the distance above the earth's surface where the acceleration due to gravity is $0.98~m/s^2$.
(equation 2):$\frac{G~M}{(R+h)^2} = 0.98~m/s^2$
We can divide equation 1 by equation 2.
$\frac{(R+h)^2}{R^2} = 10$
$R+h = \sqrt{10}~R$
$h = (\sqrt{10}-1)~R$
$h = (\sqrt{10}-1)(6380~km)$
$h = 13,800~km$
At a distance of 13,800 km above the earth's surface, the acceleration due to gravity is $0.98~m/s^2$.
