Forming Greatest and Smallest Number with Repetitive Digits.

FORMING GREATEST AND SMALLEST NUMBER WITH REPETITIVE DIGITS:

DIGITS REPETITING  TWICE IN THE NUMBER :

(a) Forming Greatest Number:

In Forming a greatest number with the Repetitive digits, we need to check the given digits: we need to follow three steps.

(i) The number of digits given, by which the greatest place value occupied by the greatest digit can be found.

(ii)  The digits are written in Descending order.

(iii) The greater digit is written twice ( two times ) : first in the greatest  place value and the same greater number is written in the next greater place value.

The number other than greater number is written in next corresponding place values.By writing the greater number twice, one of the digit is left out from the given digits.we can simply leave out that remained number.

The greater digit in the given digits occupies greatest place value twice ,the next greater digit occupies the next place value and so on.

1) Digits: 1 , 3, 7 , 8 .

Answer:

Step - 1: The  number of digits = 4 ;

 So the greatest place value is THOUSANDS (Th).

Thousands     (Th)

Hundreds     (H)

Tens   (T)

Ones   (O)

 

 Step-2 : The Descending order of the given digits: 8 , 7 , 3, 1.

                    8 > 7 > 3 > 1 .

 Step -3: The greater number in the given digit is : 8 ; which is repeated twice in the Place value System.

i.e; digit  8 is written in Thousands (Th) and the next greater place is Hundreds (H).The next greater digits are 7 and 3 , which are put in Tens(T) and Ones(O) place value. 

The remaining digit '1 '  can leaved out.No need to represent in place value.

Thousands     (Th)	Hundreds     (H)	Tens   (T)	Ones   (O)
8	8	7	3

The greatest number formed with the given digits ,repeating twice.

 8873.

 

2) Digits : 6 , 4 , 3 , 9 , 5 , 1.

Answer:

Step – 1:  The number of digits = 6   

So , the greatest place value is Lakhs(L).

Lakhs    (L)

TenThousands       (TTh)

Thousands     (Th)

Hundreds     (H)

Tens   (T)

Ones   (O)

 Step – 2 : The Descending order of the digits : 9 > 6 > 5 > 4 > 3 > 1.

Step – 3: The digit 9, which is greater need to put in two place values. i.e; Lakhs(L) , TenThousands(TTh) ,  the next greater numbers are placed in next place values.

We leave out the remained digit '1' from the given digits.

Lakhs    (L)	TenThousands       (TTh)	Thousands     (Th)	Hundreds     (H)	Tens   (T)	Ones   (O)
9	9	6	5	4	3

 Thus the greatest number formed is :  9,96,543.

 

Note: If the greater digit  to be repeated Thrice, then the greater is digit is to put in First three greater place values ,followed by the next greater numbers in the corresponding Place values.

  

(b) Forming Smallest Number:

In Forming a smallest number with the given digits, we need to check the given digits:

(i) The number of digits given, by which the greatest place value occupied by the smallest digit can be found.

(ii)  The digits are written in Ascending order.

(iii) The Smallest  number is to put in the greatest place value.The same greater value is to be put in the next greater place value.The next smaller digits is to be put in the next corresponding place values.

If  digit Zero ‘0’ is found in the given digits, then it should not put in the greatest place value,as the digit ‘0 ‘ in the left most of the number,the number  has no value.

So, we have to find the next greater digit than Zero i.e; next smallest number and is to be put first in the greatest place value . Then digit Zero is to put in the next place values two times .The next greater digits occupies the next corresponding place values.     

 

1) Digits: 5 , 8 ,3 , 0

Answer:

Step – 1 :  The number of digits = 4 .

 So, the greatest place value is Thousands(Th).

 

Thousands     (Th)

Hundreds     (H)

Tens   (T)

Ones   (O)

Step-2: The Ascending order of the digits: 0 < 3 < 5 < 8 .

Step – 3: Here, digit 0 is their, so we need to check the next smaller number other than digit ‘0’. i.e;  3.

The smaller digit 3 is to put in the greatest place value i.e : in Thousands place.Then Digit ‘ 0 ‘ is written in  the next two place values.i.e; Hundreds(H) and Tens(T) place value. The next smaller digit is 5 ,is written in Ones(O) place value.

We leave out the remained digit '8'.

Thousands     (Th)	Hundreds     (H)	Tens   (T)	Ones   (O)
3	0	0	5

Thus the Smallest number formed : 3,005.

 

2) Digits: 6 , 3 , 8.

Answer:

Step – 1: The number of digits = 3.

So , the greatest place value is Hundreds(H) place.

Hundreds  (H)

Tens  (T)

Ones (O)

 Step – 2 : The Ascending order of the digits: 3 < 6 < 8 .

Step – 3 : Here, the smallest digit is ‘ 3 ‘ , which is repeated twice in place values.i.e; Hundreds(H) and Tens(T).we leave out the remained Digit ' 8' . 

Hundreds  (H)	Tens  (T)	Ones (O)
3	3	6

 Thus the smallest number is :  336.

The Table shows Greatest and Smallest number with digits repeating twice in the number formed:

S.No	DIGITS	SMALLEST NUMBER	GREATEST NUMBER
1	3,9,2,1	1,123	9,932
2	6,7,8,3	3,367	8,876
3	5,0,3,1,9	10,035	99,531
4	8,0,3,6,4	30,046	88,643