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.

**For Example:**

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:**

**(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.

**Related Concept **

**Formation of Numbers.****Finding Out the Numbers****Names of the Numbers.****Numbers Showing on Spike Abacus.****1 Digit Number on Spike Abacus.****2 Digits Number on Spike Abacus.****3 Digits Number on Spike Abacus.****4 Digits Number on Spike Abacus.****5 Digits Number on Spike Abacus.****Large Number.****Place Value Chart.****Place Value.****Problems Related to Place Value.****Expanded form of a Number.****Standard Form.****Comparison of Numbers.****Example on Comparison of Numbers.****Successor and Predecessor of a Whole Number.****Arranging Numbers.****Formation of Numbers with the Given Digits.****Formation of Greatest and Smallest Numbers.****Examples on the Formation of Greatest****and the Smallest Number.****Rounding off Numbers.**

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