Understanding the Problem
To find the smallest 6-digit number using the digits 7, 6, 5, 0, 8 without repetition, we need to consider the arrangement of these digits carefully.
Steps to Identify the Smallest Number
- Count the Digits: We have the digits 7, 6, 5, 0, and 8. There are 5 digits available.
- Forming a 6-digit Number: Since we only have 5 digits, we will have to repeat one digit. The optimal choice is to use '0' again, as it is the smallest digit.
- Arrange the Digits: The goal is to place the digits in ascending order, while ensuring the first digit is not '0' (as that would not yield a valid 6-digit number).
Constructing the Number
- First Digit: The smallest non-zero digit available is '5', which will be the first digit.
- Remaining Digits: After placing '5' at the start, we can arrange the digits in ascending order. The remaining digits are 0, 6, 7, and 8.
- Final Arrangement: We can now form the number as follows:
- Place '0' next (as it is the smallest)
- Then '6', '7', and '8'
- Lastly, repeat '0' at the end.
Resulting Smallest Number
The smallest 6-digit number we can create is 500067.
Conclusion
By strategically choosing the first digit and arranging the remaining digits in ascending order, we can effectively determine the smallest 6-digit number using the given digits.