Question

Write the smallest and greatest number using each of the digits $3,6,0,8,7,9$ exactly once. Express the difference between the two numbers thus formed in expanded form.

Answer 1

Step 1 : Form the smallest and greatest number.

Given digits: $3,6,0,8,7,9$

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 the smallest number,

$0<3<6<7<8<9$

Now smallest number is $036789=36789$

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.

Now, for the greatest number

$9>8>7>6>3>0$

So, the greatest number is $987630$

Step 2 : Find the difference.

Difference $=$ greatest number $-$ smallest number

$=987630-306789$

So we get,

$\text{L}\text{TTH}\text{TH}\mathrm{H}\mathrm{T}\mathrm{O}615121098\cancel{7}\cancel{6}\cancel{3}\cancel{0}-306789680841$

Now, expanded form of the difference is $680841=6\times 100000+8\times 10000+0\times 1000+8\times 100+4\times 10+1\times 1$

Hence, the required expanded form is shown above.