if a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with what denominator?
100
1,000
99
999
If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with a denominator of 999.
If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with a denominator of 999.
To determine the denominator of a rational number, we need to consider the number of digits in the repeating cycle of the decimal.
In this case, the repeating cycle has three digits. To convert a repeating decimal to a fraction, we write an equation with the given decimal as "x" and the repeating cycle of digits as "y".
To find the denominator, we count the number of digits in the repeating cycle and create a fraction with that many nines in the denominator.
In this case, the repeating cycle has three digits, so the denominator will be a number with three nines, which is 999. Therefore, the rational number will have a denominator of 999.