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

up to seven digits long
up to seven digits long

infinitely long
infinitely long

any finite length
any finite length

Answer 1

up to six digits long.

Reason: the decimal period equals the order of 10 modulo 7, which is 6 (10^6 ≡ 1 mod 7 but no smaller positive power ≡1), so repeating cycles have length at most 6 (and for 1/7,2/7,...,6/7 it is exactly 6).