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
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
I apologize for the confusion in my previous response. The correct answer is "infinitely long." The repeating cycle of a repeating decimal can be as long as necessary when the denominator of the rational number is 7.
up to six digits long
are you sure?
The repeating cycle of a repeating decimal with a denominator of 7 could be up to six digits long.
To find out how many digits long the repeating cycle of a repeating decimal can be when the denominator of the rational number is 7, we can follow a simple rule.
First, we need to understand that the repeating cycle of a decimal occurs when we perform long division. In this case, we divide 1 by 7.
To perform the long division, we write 1 as the numerator and 7 as the denominator, then carry out the division:
```
0.142857...
```
As we can see, the decimal expansion of the fraction 1/7 repeats after 6 digits. The repeating cycle is: 142857.
Thus, the correct answer is "up to six digits long".