To find the largest and smallest 4-digit numbers that can be formed using the digits 4, 0, 3, and 7, we need to arrange these digits in specific ways.
Finding the Largest 4-Digit Number
To create the largest possible 4-digit number, we should start with the highest digits and arrange them in descending order. The digits we have are 4, 0, 3, and 7. Arranging these from largest to smallest gives us:
- 7 (largest)
- 4
- 3
- 0 (smallest)
So, the largest 4-digit number we can form is 7430.
Finding the Smallest 4-Digit Number
To create the smallest possible 4-digit number, we have to ensure that the first digit is not 0 (since we want a valid four-digit number). Therefore, we can only start with the digits 3 or 4. To create the smallest number, we should start with the smallest of these valid options, which is 3, followed by 0, and then the remaining digits in increasing order:
- 3 (first digit)
- 0 (next smallest)
- 4
- 7
Thus, the smallest 4-digit number we can form is 3047.
Summary
From the digits 4, 0, 3, and 7:
- The largest 4-digit number is: 7430
- The smallest 4-digit number is: 3047