Fading Gradient in a Recurrent Net

A scalar linear recurrent unit updates its state as $h_t = 0.9\,h_{t-1} + x_t$. Backpropagation through time multiplies the local derivative $\partial h_t/\partial h_{t-1}$ at every step.

What is $\partial h_{100}/\partial h_0$? Give the answer as a number (at least 7 significant figures).