How many digits long could the repeating cycle of a repeating decimal be if the denominator of the rational number is 7?(1 point) Responses any finite length any finite length up to seven digits long up to seven digits long up to six digits long up to six digits long infinitely long

Answer 1

For a repeating decimal derived from a rational number, the length of the repeating cycle can be determined by the denominator when the rational number is in simplest form. When the denominator is 7, the repeating cycle's length can be at most the Euler's totient function of 7 (which is 6), since 7 is prime.

Thus, the repeating decimal for a fraction with a denominator of 7 can have a repeating cycle that is up to 6 digits long.

Therefore, the correct response is up to six digits long.