There are 11 numbers divisible by 9 between 100 and 200.
According to the provided reference, the first three-digit number between 100 and 200 divisible by 9 is 108, and the last one is 198. The reference states that the total count is calculated as (198 – 99) / 9 = 99 / 9 = 11.
Here's a breakdown of how we arrive at this answer:
- Finding the First Multiple: The smallest multiple of 9 greater than 100 is 108 (9 x 12).
- Finding the Last Multiple: The largest multiple of 9 less than 200 is 198 (9 x 22).
- Determining the Number of Multiples: To find the number of multiples, we calculate (198 - 108)/9 + 1. Which simplifies to 90/9 + 1 = 10 + 1= 11. Therefore, 11 numbers between 100 and 200 are divisible by 9.
- Verification: The reference confirms this by using a simplified formula (198-99)/9 = 99/9 = 11
- This works because we want to know how many multiples there are from 108 (which is 9 12) to 198 (which is 9 22). If we subtract 99 (which is 9 11) from 198, we get the number of multiples of 9 starting at the multiple after 99*. Then divide by 9 to get the count.
Here's a list of those multiples:
- 108
- 117
- 126
- 135
- 144
- 153
- 162
- 171
- 180
- 189
- 198
