Find the sum and difference of the largest 4 digit number.
ANSWER
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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$ $\left( {ii} \right)$ Difference (D) $ \Rightarrow D = 9999 - 1000 = 8999$ So this is the required sum and difference of largest and smallest 4 digit numbers. So this is the required answer.
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 doesnâ€™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.