To find the difference between the largest and smallest 5-digit numbers formed using the digits 6, 0, 9, and 5 with 0 repeated twice, let's break it down step by step.

Step 1: Identify the Largest 5-Digit Number

To form the largest possible 5-digit number, arrange the digits in descending order. We need to choose five digits in total, so we will use 6, 9, 5, 0, and 0.

• The largest 5-digit number using these digits is: 96500

Step 2: Identify the Smallest 5-Digit Number

To form the smallest possible 5-digit number, arrange the digits in ascending order. However, remember that a number cannot start with 0, so we need to adjust the digits to ensure the smallest number is still valid:

• Start with the smallest non-zero digit, which is 5.
• The smallest 5-digit number using these digits is: 50069

Step 3: Calculate the Difference

Now, subtract the smallest number from the largest number:

$96500 - 50069 = 46431$

Final Answer

The difference between the largest and smallest 5-digit numbers formed by the digits 6, 0, 9, 5 when 0 is repeated twice is 46,431.

Would you like more details or have any questions? Here are some related problems:

1. What is the largest and smallest 5-digit number using the digits 1, 2, 3, 0, 0?
2. How would the result change if you could not repeat any digits?
3. What is the sum of the largest and smallest 5-digit numbers formed by the digits 3, 1, 4, 0, and 0?
4. What is the largest 6-digit number that can be formed using 6, 0, 9, and 5 with repetition allowed?
5. What is the smallest 4-digit number using the digits 6, 0, 9, and 5 with repetition allowed?

Tip: When forming numbers, always start arranging digits in descending order for the largest number and ascending order (with a non-zero digit at the start) for the smallest number.