There are 1000 four-digit numbers that are divisible by 9.
Here's how to determine that:
-
Smallest four-digit number divisible by 9: The smallest four-digit number is 1000. Dividing 1000 by 9 gives approximately 111.11. Therefore, the smallest four-digit number divisible by 9 is 112 * 9 = 1008.
-
Largest four-digit number divisible by 9: The largest four-digit number is 9999. Dividing 9999 by 9 gives 1111 with no remainder. Thus, 9999 is divisible by 9.
-
Counting the numbers: We want to find the number of multiples of 9 between 1008 and 9999, inclusive. This is equivalent to finding the number of integers between 112 and 1111, inclusive.
- The number of integers is 1111 - 112 + 1 = 1000.
Therefore, there are 1000 four-digit numbers divisible by 9.
