# 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. We have learnt already that the greatest number is formed by arranging the given digits in descending order and the smallest number by arranging them in ascending 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.

If one of the given digit is 0, we never write the digit 0 at the extreme left place, instead we write 0 at the second place from the left to get the smallest number.

Examples on Formation of Greatest and Smallest Numbers:

1. Form the greatest and smallest number using the digits 9, 3, 7, 5.

 To Form the Greatest Number To Form the Smallest Number Greatest number should have greatest digit in the thousands place that is 9. Smallest number should have smallest digit in the thousands place that is 3. The next greatest digit in the hundreds place that is 7. The next smallest digit in the hundreds place that is 5. The next greatest digit in the tens place that is 5. The next smallest digit in the tens place that is 7. The smallest digit in the ones place that is 3. The next smallest digit in the ones place that is 9. So, the greatest number is 9753 So, the smallest number is 3579 Here, digits are arranged in descending order Here, digits are arranged in ascending order.

2. Form the greatest and the smallest numbers using the digits.

6, 8, 1, 0, 9, 5, 4, 2.

Solution:

We arrange the given digits in descending order to form the greatest number. Hence, the greatest number is 9,86,54,210.

We arrange the given digits in ascending order to form the smallest number. Hence, the smallest number is 1,02,45,689.

Solved examples on Formation of Greatest and Smallest Numbers:

3. 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.

4. 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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