Forming Smallest and Greatest Number from the Given Digits

We will learn how to form the smallest and greatest number from the given digits.

We know that the greatest number is formed by arranging the given digits in descending order.

Let us take digits 4, 2 and 8

We arrange these digits in descending order to form the greatest number.

Descending order: 8, 4, 2

We write the smallest digit 2 in ones place and next greater number 4 is written in tens place. The greatest digit 8 is written in hundreds place. So, the greatest number with the given digits is 842.

H T O

8 4 2

Now, let us make the smallest number with the above given three digits 4, 2 and 8.

We arrange the digits in ascending order to form the smallest number.

Ascending order: 2, 4, 8

We write the smallest number 2 in the hundreds place. The next smallest number 4 is written in the tens place and the greatest number in ones place. 248 is the smallest number formed with the given digits.

H T O

2 4 8

We know that we do not write 0 in the extreme left of any number. Therefore, when 0 is one of the digit, we place 0 at ones place to form the greatest number.

Let us consider there digits 2, 0, 8.

We know that the greatest number is formed by arranging the given digits in descending order.

We arrange 2, 0, 8 in descending order: 8, 2, 0

So, the greatest 3-digit number is 820.

We write the smallest digit in ones place and next greater number in order are written in tens and hundreds place.

Let us see how many different 3 –digit numbers can be formed using the above given digits.

208, 802, 820 and 280

208 is the smallest number. So, to make smallest number, we place 0 in tens place.

We write the smallest digit in tens place. The greatest digit is written in ones place.

H T O

2 0 8

Let us arrange these numbers in ascending and descending order:

Ascending order: 208, 280, 802, 820

Descending order: 820, 802, 280, 208

Questions and Answers on Forming Smallest and Greatest Number from the Given Digits:

1. Form the smallest and greatest 3-digit numbers using the given digits only once.

	Digits	Smallest Number	Greatest Number
(i)	3, 9, 1	_____	_____
(ii)	1, 6, 8	_____	_____
(iii)	5, 5, 8	_____	_____
(iv)	1, 0, 9	_____	_____
(v)	6, 9, 0	_____	_____

Answer:

(i) 139, 931

(ii) 168, 861

(iii) 558, 855

(iv) 109, 910

(v) 609, 960

2. Write all possible numbers using the given digits once and arrange them in descending order.

(i)	2, 1, 8	_____	_____
(ii)	8, 5, 7	_____	_____
(iii)	4, 0, 8	_____	_____
(iv)	9, 8, 4	_____	_____
(v)	3, 7, 8	_____	_____
(vi)	6, 7, 7	_____	_____

Answer:

(i) Possible numbers: 218, 281, 128, 182, 812, 821

Arrange in descending order : 821, 812, 281, 218, 182, 128

(ii) Possible numbers: 857, 875, 758, 785, 578, 587

Arrange in descending order: 875, 857, 785, 758, 578, 587

(iii) Possible numbers: 408, 480, 804, 840

Arrange in descending order: 840, 804, 480, 408

(iv) Possible numbers: 984, 948, 498, 489, 849, 894

Arrange in descending order: 984, 948, 894, 849, 498, 489

(v) Possible numbers: 378, 387, 783, 738, 837, 873

Arrange in descending order: 873, 837, 783, 738, 387, 378

(vi) Possible numbers: 677, 767, 776

Arrange in descending order: 776, 767, 677

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