If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with what denominator? (1 point)
Responses
1,000
1,000
99
99
100
100
999
999
If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with a denominator of 99.
To determine the denominator of a rational number equivalent to a repeating decimal with a repeating cycle of three digits, we need to count the number of digits in the repeating cycle.
In this case, the repeating cycle has three digits. To convert a repeating decimal to a rational number, we set up an equation where the repeating digits form the numerator and the denominator is a series of nines with the same number of digits as the repeating cycle.
Since the repeating cycle has three digits, the denominator will consist of a series of nines with three digits. Therefore, the correct answer is 999.