Step 1: Determine the Range of Numbers We are looking for numbers between 99 and 1000, which are all 3-digit numbers. So, the numbers must be between 100 and 999.

Step 2: Identify Numbers with 8 in the Unit's Place For a number to have the digit 8 in the unit's place, the number must be of the form: $X8$, where $X$ can be any digit from 1 to 9 for the hundreds place (since the number is between 100 and 999), and from 0 to 9 for the tens place.

Step 3: Count the Possible Numbers The hundreds place ($X$) can have any value from 1 to 9, giving us 9 choices. The tens place can have any value from 0 to 9, giving us 10 choices. The unit's place is fixed as 8.

Thus, the total number of such numbers is: $9 \times 10 = 90$

Final Answer: The number of numbers between 99 and 1000 such that the digit 8 occupies the unit's place is 90.

Correct Answer: C. 90