Introduction
When faced with the task of forming the largest and smallest 5-digit numbers from a given set of digits, it#39;s important to understand the principles involved. In this article, we will explore how to arrange the digits 8, 0, 7, 3, and 4 to create the greatest and smallest 5-digit numbers possible. Let#39;s dive into the process step by step.
The Greatest 5-Digit Number
When forming the greatest 5-digit number from the digits 8, 0, 7, 3, and 4, the strategy is straightforward. We need to place the largest possible digit in the highest place value position and continue in descending order.
Begin with the largest digit: 8. Place 8 in the ten-thousands place. Next, choose the second-largest available digit: 7. Place 7 in the thousands place. Follow the next largest digit: 4. Place 4 in the hundreds place. Then, select the next largest digit: 3. Place 3 in the tens place. The smallest remaining digit: 0. Place 0 in the units place.This arrangement gives us the number 87,430 as the greatest 5-digit number that can be formed with these digits.
The Smallest 5-Digit Number
For the smallest 5-digit number, we follow the opposite strategy. Here, we place the smallest non-zero digit in the ten-thousands place to avoid leading zeros, and then continue in ascending order.
Begin with the smallest non-zero digit: 3. Place 3 in the ten-thousands place. Next, choose the smallest remaining digit: 0. Place 0 in the thousands place. Follow the next smallest digit: 4. Place 4 in the hundreds place. Then, select the next smallest digit: 7. Place 7 in the tens place. The largest remaining digit: 8. Place 8 in the units place.This arrangement gives us the number 30,478 as the smallest 5-digit number that can be formed with these digits.
Theoretical Considerations
The theoretical answer for the smallest 5-digit number can be 03478. However, since we are dealing with five-digit numbers, we need to ensure there is no leading zero. Therefore, the smallest number that meets the criteria is 30,478.
Conclusion
In conclusion, understanding how to arrange the digits to form the greatest and smallest 5-digit numbers is a fundamental skill in number theory and can be applied in various mathematical and real-world scenarios. Whether you#39;re forming codes, creating secure passwords, or simply solving a math problem, knowing the principles behind these arrangements can be extremely useful.