How many digits long could the repeating cycle of a repeating decimal be if the denominator of the rational number is 7?(1 point)

Question

Responses

up to seven digits long
up to seven digits long

up to six digits long
up to six digits long

any finite length
any finite length

infinitely long
infinitely longHow 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 seven digits long
up to seven digits long

up to six digits long
up to six digits long

any finite length
any finite length

infinitely long
infinitely long

Answer 1

The repeating cycle of a repeating decimal for a fraction with a denominator of 7 can be up to 6 digits long. This is because the length of the repeating cycle of a decimal is determined by the smallest power of 10 that, when reduced modulo the denominator, gives a remainder of 1.

For the denominator 7, the possible lengths of the repeating cycle can be found by determining the order of 10 modulo 7, which is 6. Hence, the correct answer is:

up to six digits long.