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

up to six digits long
up to six digits long

infinitely long
infinitely long

any finite length
any finite length

up to seven digits long
up to seven digits long
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Answer 1

The length of the repeating cycle of a repeating decimal is determined by the denominator of the rational number when it is expressed in lowest terms. For a denominator of 7, the maximum length of the repeating part of the decimal can be at most \(7 - 1 = 6\) digits long, because the repeating cycle length of a fraction with a prime denominator \(p\) is at most \(p-1\).

Thus, the correct response is:

**up to six digits long**.