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

infinitely long
infinitely long

up to seven digits long
up to seven digits long

any finite length
any finite length

up to six digits long

Answer 1

The repeating cycle of a repeating decimal formed by a rational number with a denominator of 7 can have a maximum length of 6 digits. This is because the length of the repeating section of a decimal is determined by the properties of the denominator when expressed in its simplest form relative to 10.

In this case, since 7 is a prime number that does not divide 10, the repeating decimal can have a maximum length of \( 7 - 1 = 6 \) digits.

Therefore, the correct answer is: up to six digits long.