There are 180 numbers between 100 and 999 that are divisible by 5.
According to Theorem 9.1.1, the total number of integers from 100 through 999 is calculated as 999 - 100 + 1 = 900. The reference also states that 180 of these numbers are divisible by 5.
Here's a breakdown to help understand why:
- The first number in the range (100-999) divisible by 5 is 100.
- The last number in the range divisible by 5 is 995.
- To find the total, we can consider this an arithmetic sequence where:
- First term (a) = 100
- Common difference (d) = 5
- Last term (l) = 995
We can use the formula to find the number of terms in an arithmetic sequence:
n = (l - a)/d + 1
Therefore, n = (995 - 100) / 5 + 1
n = 895 / 5 + 1
n = 179 + 1
n = 180
This method confirms the provided reference, demonstrating that there are 180 numbers between 100 and 999 that are divisible by 5.
