How many power of 2?

$\large{0.\quad 000001\quad 000002\quad 000004\quad 000008 \ldots}$

The Above shows the first few digits of the decimal representation of the fraction $\Large{\frac { 1 }{ 999,998 } }$ . If we split the digits into partitions of 6, we can see that the numbers are all powers of 2. Inclusive of $2^0=1$ , how many powers of 2 can we find before the pattern breaks off?

Bonus :- Generalize for ${\dfrac{1}{10^k-2}}$ and $\dfrac{1}{10^{k}-n}$ , where $k$ and $n$ are positive integers.

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