Question

If a repeating decimal has a repeating cycle of three digits, it will covert to a rational number with what denominator?
A. 1,000
B. 999
C. 100
D. 99

Answer 1

If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with a denominator of 999.

The repeating decimal can be expressed as the fraction where the numerator is the repeating cycle (represented by the three digits), and the denominator is the number of repeating digits raised to the power of the length of the repeating cycle. In this case, the repeating decimal has a repeating cycle of three digits, so the denominator is $10^3 - 1 = 999$.

Therefore, the answer is $\boxed{\text{B. 999}}$.