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
infinitely long
any finite length
up to seven digits long
Convert 0.27¯¯¯¯¯ to a rational number in simplest form.(1 point)
Responses
The repeating cycle of a repeating decimal with a denominator of 7 can be up to 6 digits long.
To determine the length of the repeating cycle of a repeating decimal when the denominator of the rational number is 7, we can use a mathematical method.
First, we need to divide 1 by 7: 1/7 = 0.142857...
The repeating cycle in this case is 142857, which consists of 6 digits. So, the correct answer is up to six digits long.
To obtain this answer, you can use long division to divide 1 by 7, and observe the repeating pattern that emerges.