How many digits long could the repeating cycle of a repeating decimal be if the denominator of the rational nu

Question

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

infinitely long
infinitely long

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
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GPT-5 mini · Answer

Up to six digits long.

Reason: the period equals the multiplicative order of 10 modulo 7, which divides φ(7)=6. Example: 1/7 = 0.\overline{142857} has a 6-digit repeat.

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