If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with what denominator?(1 point)
A repeating decimal with a repeating cycle of three digits will convert to a rational number with a denominator of 999.
To determine the denominator of a repeating decimal with a repeating cycle of three digits, we can follow these steps:
Step 1: Identify the repeating cycle of three digits in the decimal.
Step 2: Count the number of digits in the repeating cycle. In this case, it's three digits.
Step 3: Write the repeating decimal as a fraction. To do this, we assign the repeating cycle as the numerator (with one digit representing each place value of the numerator) and assign the denominator as an integer that consists of the digit 9 repeated the same number of times as the length of the repeating cycle. In this case, the denominator will be 999.
Step 4: Simplify the fraction if possible.
Therefore, the repeating decimal with a repeating cycle of three digits will convert to a rational number with a denominator of 999.