Rational number with more than ten digits

The period of a periodic sequence of digits can be as large as you like. To see this, multiply the number by $10^T$, where $T$ is the period, and then subtract the original number. Since this is definitely a whole number $n$ – the repeating parts of the sequence cancel out – the original must have been a rational number, specifically $n/(10^T-1)$.

This also happens for "ordinary" rational numbers. For instance, $\frac1{17}$ has a period of 16 digits, and $\frac1{983}$ has a period of 982 digits. Look up "full reptend prime" or "long prime" for more information about them.

Short answer:

$$\dfrac1{17}=0.\color{green}{0588235294117647}0588235294117647\color{green}{0588235294117647}0588235294117647\cdots$$

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Also think that you are free to take any finite sequence of digits and repeat it forever, you will always get a rational number.