# Formation of Greatest and Smallest Numbers

In formation of greatest and smallest numbers we know the procedure of arranging the numbers in ascending and descending order. The position of the digit at the extreme left of a number increases its place value. So the greatest digit should be placed at the extreme left side of the number to enhance its value.

For example:

(i) Suppose we have to form the greatest number with the digits 6, 5, 2, 9. We know that a four digit number has four places, i.e., thousands, hundreds, tens and ones or units from left to right as Th, H, T, O. If greatest to lowest digits are placed at these places in descending order, we get the greatest number and if placed in ascending order, we get the smallest number.

Observe the formation of greatest and smallest numbers so formed are:

Th      H       T       O
Greatest number           9       6       5       2

Smallest number           2       5       6       9

To get the greatest number, the greatest digit 9 is placed at the highest valued place, i.e., thousands-place, next smaller digit 6 at hundreds-place, still smaller digit 5 at ten's place and the smallest digit 2 at one's or units place.

Thus, the greatest number is 9652.

To get the smallest number, the smallest digit 2 is placed at thousands-place, next greater digit 5 at hundred’s place, still greater digit 6 at ten's place and greatest digit 9 at one's or units place.

Thus, the smallest number is 2569.

(ii) Suppose we have to form the greatest number with the digits 8, 1, 4, 7. We know that a four digit number has four places, i.e., thousands, hundreds, tens and ones or units from left to right as Th, H, T, O. If greatest to lowest digits are placed at these places in descending order, we get the greatest number and if placed in ascending order, we get the smallest number.

Observe the formation of greatest and smallest numbers so formed are:

Th      H       T       O
Greatest number           8       7       4       1

Smallest number           1       4       7       8

To get the greatest number, the greatest digit 8 is placed at the highest valued place, i.e., thousands-place, next smaller digit 7 at hundreds-place, still smaller digit 4 at ten's place and the smallest digit 1 at one's or units place.

Thus, the greatest number is 8741.

To get the smallest number, the smallest digit 1 is placed at thousands-place, next greater digit 4 at hundred’s place, still greater digit 7 at ten's place and greatest digit 8 at one's or units place.

Thus, the smallest number is 1478.

In formation of greatest and smallest numbers these are the procedure of arranging the numbers in ascending and descending order.

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