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

Answer 1

The repeating cycle of a repeating decimal resulting from a rational number is determined by the denominator when the fraction is in its simplest form. Specifically, the length of the repeating cycle can be at most equal to the denominator minus one, or equal to the length of the recurring part of the decimal.

For a denominator of 7, the maximum length of the repeating cycle could be up to 6 digits long. This is because the decimal representation of a fraction with a prime denominator can repeat for a length up to the denominator minus one (which in this case is 7 - 1 = 6).

So the correct response is:

up to six digits long.