The exact number of three-digit numbers lying between 100 and 999 inclusive is 900.
Understanding Three-Digit Numbers
Three-digit numbers are whole numbers that consist of exactly three digits. The smallest three-digit number is 100, and the largest is 999. This range encompasses all integers from one hundred up to nine hundred ninety-nine.
The Exact Count: 900 Numbers
When asked about the number of integers within a given range that is "inclusive," it means that both the starting and ending numbers of the range are included in the count. In this case, we are counting all numbers from 100 to 999, including both 100 and 999 themselves.
Reference Confirmation
As confirmed by educational resources like BYJU'S, the total count for this range is indeed 900. According to their explanation, "As we already discussed, the three digits numbers are from 100 (hundred) to 999 (nine hundred ninety-nine)... Hence, there are 900 three-digit numbers in total." This statement directly addresses the question. For more details, you can refer to the Three Digits Numbers - List 100 to 999, How Many? on BYJU'S.
How to Calculate (Last - First + 1)
A common method to find the count of numbers in an inclusive range is to use the formula:
Count = (Last Number - First Number) + 1
Let's apply this to our range:
- First Number: 100 (the smallest three-digit number)
- Last Number: 999 (the largest three-digit number)
Calculation:
Count = (999 - 100) + 1
Count = 899 + 1
Count = 900
This calculation confirms the total of 900 three-digit numbers.
Illustrative Range
Here's a simple representation of the range:
| Description | Value |
|---|---|
| Smallest Three-Digit Number | 100 |
| Largest Three-Digit Number | 999 |
| Total Count (Inclusive) | 900 |
Why "Inclusive" Matters
The term "inclusive" is crucial because it dictates whether the boundary numbers are part of the count. If the question had asked for numbers between 100 and 999 exclusive, it would mean numbers like 101, 102, ..., 998, resulting in a different count (998 - 101 + 1 = 898). However, since the question explicitly states "inclusive," both 100 and 999 are counted, ensuring the result is 900.
