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
infinitely long
infinitely long
any finite length
any finite length
up to seven digits long
up to seven digits long
The repeating cycle of a repeating decimal with a denominator of 7 can be up to 6 digits long.
The repeating cycle of a repeating decimal with a denominator of 7 could be up to six digits long.
The repeating cycle of a repeating decimal is determined by the length of the repeating block. To find the length of the repeating cycle, we need to understand the relationship between the denominator of the rational number and the repeating cycle.
In this case, the denominator of the rational number is 7. Since 7 is a prime number and it is not divisible by any other prime number except itself, the repeating cycle of the decimal representation will be at most 6 digits long.
To verify this, you can perform long division by dividing the numerator of the rational number by 7. The remainder at each step will determine the repeating cycle. Eventually, you will find that the remainder repeats itself. If the repeating block is longer than 6 digits, it means that the remainder did not repeat, which is not possible when dividing by a prime number like 7.
Therefore, the answer is: "up to six digits long."