if a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with what denominator?

Question

a. 1,000
b. 100
c. 99
d. 999

Answer 1

The answer is d. 999.

To convert a repeating decimal with a repeating cycle of three digits to a rational number, we place the repeating cycle over a denominator that consists of as many nines as there are digits in the cycle.

In this case, since the repeating cycle has three digits, the denominator would consist of three nines, which is 999.