The length of the repeating cycle of a repeating decimal is determined by the denominator of the rational number when expressed in simplest form. For any denominator that is coprime to 10, the maximum length of the repeating cycle can be found by calculating the order of 10 modulo that denominator.
In the case of 7, we can check the decimal expansion of fractions with a denominator of 7.
For example:
- \( \frac{1}{7} = 0.\overline{142857} \)
- \( \frac{2}{7} = 0.\overline{285714} \)
- \( \frac{3}{7} = 0.\overline{428571} \)
- \( \frac{4}{7} = 0.\overline{571428} \)
- \( \frac{5}{7} = 0.\overline{714285} \)
- \( \frac{6}{7} = 0.\overline{857142} \)
From this, we see the repeating cycle has a length of 6 digits (142857).
Therefore, the correct answer is: up to six digits long.