Form the greatest and the smallest 4 digit numbers using the given digits without repetition 7, 0, 4 and 2.

To form the greatest and smallest four-digit numbers using the digits 7, 0, 4, and 2 without repetition, we need to consider the placement of each digit carefully. Let's break this down step by step.

Creating the Largest Four-Digit Number

To construct the largest number, we should start with the highest digits in the most significant places. The digits we have are 7, 0, 4, and 2. Here’s how we can arrange them:

• The highest digit is 7, so we place it first.
• Next, we have 4, 2, and 0 left. The next highest digit is 4, so we place it second.
• Now, we have 2 and 0 remaining. The next highest digit is 2, so we place it third.
• Finally, we place 0 in the last position.

Putting it all together, the greatest four-digit number we can form is 7420.

Forming the Smallest Four-Digit Number

Now, let’s focus on creating the smallest four-digit number. For this, we need to start with the smallest non-zero digit in the first position to ensure it remains a four-digit number. Here’s the process:

• The smallest non-zero digit is 2, so we place it first.
• Next, we have 0, 4, and 7 left. The smallest digit among these is 0, so we place it second.
• Now, we have 4 and 7 remaining. The next smallest digit is 4, so we place it third.
• Finally, we place 7 in the last position.

Combining these digits, the smallest four-digit number we can form is 2047.

Summary of Results

In summary, using the digits 7, 0, 4, and 2 without repetition:

• The largest four-digit number is 7420.
• The smallest four-digit number is 2047.

This method of arranging digits based on their value helps ensure that we create the desired numbers effectively. If you have any more questions about number formation or any other topic, feel free to ask!