Final answer:
The length of the repeating cycle of a repeating decimal with a denominator of 7 can be up to 6 digits long.
Step-by-step explanation:
The length of the repeating cycle of a repeating decimal depends on the denominator of the rational number.
In this case, the denominator is 7, which means the repeating cycle can have a maximum length of 6 digits. This is because the repeating decimal of 1/7 is 0.142857, and the repeating cycle consists of 6 digits (142857).
Therefore, the repeating cycle of a repeating decimal with a denominator of 7 could be up to 6 digits long.