There are 90 three-digit natural numbers divisible by 10.
Understanding the Problem
This question asks us to determine the quantity of three-digit numbers (from 100 to 999) that are perfectly divisible by 10. A number is divisible by 10 if it ends in a 0.
Solution
The smallest three-digit number divisible by 10 is 100 (100/10 = 10). The largest three-digit number divisible by 10 is 990 (990/10 = 99).
To find the total number of three-digit numbers divisible by 10, we can use the formula for an arithmetic sequence:
- Number of terms = (Last term - First term) / Common difference + 1
In this case:
- First term = 100
- Last term = 990
- Common difference = 10
Therefore:
Number of terms = (990 - 100) / 10 + 1 = 890 / 10 + 1 = 90
Therefore, there are 90 three-digit natural numbers divisible by 10. This aligns with the information provided in the reference stating "So there are 90 numbers which are divisible by 10." and "∴n=90 ∴ n = 90 i.e. there are 90 3 digit numbers that are divisible by 10."
Examples
- 100
- 110
- 120
- ...
- 990
These are all three-digit numbers divisible by 10.
