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

any finite length
any finite length

infinitely long
infinitely long

up to six digits long
up to six digits long

up to seven digits long

Answer 1

Up to six digits long.

Reason: the decimal period equals the order of 10 modulo 7. 10^6 ≡ 1 (mod 7) and no smaller positive power gives 1, so the period is 6.