Counting Numbers Containing the Digit 5 from 1 to 10000
In order to understand how many numbers between 1 and 10000 contain the digit 5, we will break down the problem into manageable sections. Let's explore this step-by-step to ensure a clear and comprehensive solution.
Understanding the Problem
First, let's consider the total number of integers from 1 to 10000. There are 9999 such numbers when excluding the upper limit of 10000 itself for simplicity in calculation.
Counting Without the Digit 5
It is easier to first calculate how many numbers do not contain the digit 5 and then subtract this from the total number of integers. Let's delve into the details of the calculation:
Digit Choices
Thousands Place: Can be 0, 1, 2, 3, 4, 6, 7, 8, 9 (9 choices)
Hundreds Place: Can be 0, 1, 2, 3, 4, 6, 7, 8, 9 (9 choices)
Tens Place: Can be 0, 1, 2, 3, 4, 6, 7, 8, 9 (9 choices)
Units Place: Can be 0, 1, 2, 3, 4, 6, 7, 8, 9 (9 choices)
Total Combinations Without 5
Total combinations of numbers without the digit 5: 9 x 9 x 9 x 9 94 6561.
Total Numbers Without 5
Therefore, the total number of integers from 1 to 9999 that do not contain the digit 5 is 6561.
Counting With the Digit 5
Now, we need to find the total number of integers from 1 to 9999 that contain at least one 5. We can achieve this by subtracting the number of integers without the digit 5 from the total number of integers:
Total numbers from 1 to 9999: 9999
Total numbers without the digit 5: 6561
Thus, the total number of integers from 1 to 9999 that contain at least one 5: 9999 - 6561 3438.
Including 10000
The number 10000 does not contain the digit 5, so it does not affect our count.
Final Count
The final count of numbers from 1 to 10000 that contain at least one 5 is 3438.
Conclusion
By understanding the breakdown of digits and applying combinatorial logic, we can effectively determine the number of integers containing the digit 5 within the specified range. This method ensures a clear and accurate solution to the problem, providing valuable insights for similar digit counting scenarios.