Lower bound for the length period of the decimal expression

Question

We know (Period of the decimal expression for the rational number $\frac{1}{n}$ is at most $n-1$) that for an integer $n\geq 2$, the period length of the decimal expression for the rational number $\frac{1}{n}$ is at most $n-1$.

I am asking if there is a lower bound if $n>m$ where $m$ is given integer.

Answer 1

For $n$ relatively prime to $10$, $\dfrac1n$ repeats after $m$ digits where $n\mid10^m-1$.

Then $n<10^m$, so the period length of the decimal expression for $\dfrac1n$ is at least $ \lceil\log_{10}n\rceil$.

Answer 2

Consider that $\frac 1{100}=0.01$, which has period 0 or 1 depending on your definition of the period.

In other words, the lower bound of the period length is always 0 or 1.

Or if you want a non-zero repetition, we can always find a number with period 1. We can pick for instance something like $0.001111... = \frac 19\cdot \frac 1{100}=\frac 1{900}$.