If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with what denominator? (1 point)
A. 100
B. 1,000
C. 99
D. 999
To determine the denominator of a rational number equivalent to a repeating decimal with a repeating cycle of three digits, we use the following steps:
Step 1: Count the number of repeating digits in the cycle. In this case, the repeating cycle has three digits.
Step 2: Determine the denominator by using the formula:
Denominator = 9 × 10^(number of repeating digits) - 1
In this case, the denominator can be calculated as:
Denominator = 9 × 10^(3) - 1 = 9 × 1,000 - 1 = 9,000 - 1 = 8,999.
So, the correct answer is:
D. 999.