If a repeating decimal has a repeating cycle of 3 digits, it will convert to a rational number with what denominator?
If a repeating decimal has a repeating cycle of 3 digits, it will convert to a rational number with a denominator of 999.
To determine the denominator of a repeating decimal with a repeating cycle of 3 digits, we need to count the number of digits in the repeating cycle.
Since the repeating cycle has 3 digits, the denominator will be 9.
This is because the repeating decimal can be expressed as a fraction with the numerator being the repeating cycle (represented by the repeating digits) and the denominator being a string of nines, where the number of nines is equal to the number of digits in the repeating cycle.
For example, if the repeating cycle is 123, then the repeating decimal would be 0.123123123... In fraction form, this would be 123/999, which simplifies to 41/333.
Therefore, a repeating decimal with a repeating cycle of 3 digits will convert to a rational number with a denominator of 9.