If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with what denominator? (1 point)

Question

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

Answer 1

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.