Question

How many digits long could the repeating cycle of a repeating decimal be at the denominator of the rational number is seven what the answer be up to seven digits long any finite length or Infinitely long or up to six digits long

Answer 1

The repeating decimal form of a rational number is determined by its denominator when in simplest form. For a rational number with a denominator of 7, the decimal representation will have a repeating cycle.

The fraction \( \frac{1}{7} \) has a repeating decimal of \( 0.\overline{142857} \). The cycle "142857" has a length of 6 digits.

Therefore, the repeating cycle of the decimal for any rational number with a denominator of 7 (in simplest form) will always be a finite length of 6 digits, not infinite or up to 7 digits long.

Thus, the answer to your question is that the repeating cycle can be **up to six digits long**.