How many numbers between 101 to 200 are divisible by 9?

There are 11 numbers between 101 and 200 that are divisible by 9.

Here's how we arrive at that answer, drawing upon the information in our reference:

The reference states that the first three-digit number between 100 and 200 divisible by 9 is 108, and the last is 198. This tells us the range we're working with, since the question is from 101 to 200.
It also states that the number of multiples of 9 between 100 and 200 can be found with the equation (198-99)/9 = 99/9 = 11

• Finding the First Multiple: The smallest number after 101 that's divisible by 9 is 108. (101 / 9 = 11 with a remainder; 12 * 9 = 108).
• Finding the Last Multiple: The largest number before 200 that's divisible by 9 is 198. (200 / 9 = 22 with a remainder; 22 * 9 = 198).
• Calculating the Count: We can use the formula from the reference: (Last Multiple - First Multiple +9)/9 which is (198-108+9)/9 = 99/9=11. Alternatively, since the numbers are in an arithmetic progression, it can also be calculated using the formula [(last number - first number)/ divisor] + 1 = [(198 - 108)/9] + 1 = [90/9] + 1 = 10 + 1 = 11

Listing the Multiples

To illustrate, the multiples of 9 between 101 and 200 are:

1. 108
2. 117
3. 126
4. 135
5. 144
6. 153
7. 162
8. 171
9. 180
10. 189
11. 198

Therefore, there are 11 numbers between 101 and 200 that are divisible by 9.