Question

Find the difference between the largest and smallest number that can be formed by using each of the digits $7,3,0,9,5,4$ exactly once.

Answer 1

Step 1: Form the Largest number and smallest number.

Given digits: $7,3,0,9,5,4$

To find the greatest number using the given digits where each digit occurs only once is to arrange the digits in descending order and the number obtained will be the greatest number formed by the given digits.

For largest number ,

$9>7>5>4>3>0$

So, the largest number is $975430$

To find the smallest number using the given digits where each digit occurs only once is to arrange the digits in ascending order and the number obtained will be the smallest number formed by the given digits.

For smallest number,

$0<3<4<5<7<9$

So, the smallest number is $304579$ [ As $0$ can not be at the left end ]

Step 2 : Find the difference

Difference $=$ largest number $-$smallest number

$=975430-304579$

So we get,

$\text{L}\text{TTh}\mathrm{Th}\mathrm{H}\mathrm{T}\mathrm{O}\text{Carry-over}413121097\cancel{5}\cancel{4}\cancel{3}\cancel{0}-304579670851$

Hence, the required difference is $670851$.