# How many power of 2?

**Number Theory**Level 2

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.