Question

Find the sum and the difference of the largest and the smallest four digit numbers.

Answer 1

Hint: There are in total 10 basic digits which help formation of any digit which are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. The lowest possible 4 digit number must start from 1 and the highest possible 4 digit number must start from 9. Use this concept to get the sum and difference.

Complete step-by-step answer:
The possible digits are (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9)
Now we have to make the smallest and largest four digit numbers.
Now as we know that the number cannot start from zero otherwise the number converts into a three digit number for example (0123 = 123).
So the smallest four digit number starts from 1 and the rest of the terms are filled by the least number which is zero.
So the smallest 4 digit number is = 1000.
Now make the largest 4 digit number.
As we know in the largest 4 digit number all the places can be filled by the largest digit which is nine (9).
So the largest 4 digit number is = 9999.
Now we have to calculate the sum and difference of these two numbers.
$\left( i \right)$ Sum (S)
$ \Rightarrow S = 9999 + 1000 = 10999$

Therefore, the sum of the largest and smallest four digit numbers is 10999.
$\left( {ii} \right)$ Difference (D)
$ \Rightarrow D = 9999 - 1000 = 8999$

Therefore, the difference of the largest and smallest four digit numbers is 8999.

Note: If we have to form a 4 digits number then it can never start with 0, although 0 was the smallest of the basic digits than can form any number as 0 in the starting of digits doesn’t add up to the total number of digits while in every rest position it has equal significance as others. The same happens with 0 after the decimal place towards ending, no matter how many zeros we apply after the decimal point at the ending it never counts up.