To find the difference between the largest and smallest four-digit palindromes, let's first determine what these numbers are.
A palindrome reads the same forwards and backwards, so for a four-digit palindrome, the first and last digits must be the same, and the second and third digits must also be the same.
The largest digit in our decimal number system is 9, so the largest four-digit palindrome will have the digit 9 as both its first and last digit. Meanwhile, the smallest non-zero digit is 1, so the smallest four-digit palindrome will have the digit 1 as both its first and last digit.
Therefore, the largest four-digit palindrome is 9999 (first and last digit are 9, the second and third are also 9).
The smallest four-digit palindrome is 1001 (with the first and last digit being 1, and the second and third digit being 0, making it a four-digit number where initial zeros are not present and do not disqualify the number as a four-digit palindrome).
Now, to find the difference between these two palindromes, we will subtract the smallest from the largest:
Difference = Largest Palindrome - Smallest Palindrome
Difference = 9999 - 1001
Performing the subtraction gives us:
Difference = 8998
The correct answer is D) 8998.
