Forming Greatest and Smallest 6-Digit number using Given Digits.

FORMING GREATEST AND SMALLEST NUMBER WITH THE GIVEN DIGITS:

In some cases,the given digits from which the number to be formed are lesser than the digits in the number formed.In such case, we need to use Repetition of digits in formation of greatest and smallest number.

Form  Greatest and Smallest 6^th digit number.

1) Digits: 3,7,8,4,9  

Answer:

a) Greatest Number:

Here, the number of digits given are lesser than the digit to be formed.

So, to form greatest number with the given digits ,the greater digit is repeated.

In the given digits, the greater number is ‘9’, which is to be repeated.

Step-1: The number of digits given = 5.

The number to be formed is 6^th digit number, which need one more digit.

 Step-2: Descending Order of the given digits:  9 > 8 > 7 > 4 > 3 .    

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.

Lakhs    (L)	TenThousands       (TTh)	Thousands     (Th)	Hundreds     (H)	Tens   (T)	Ones   (O)
9	9	8	7	4	3

 

Thus the greatest number formed is :  9,98,743.

 

b) Smallest number:

The given digits are: 3,7,8,4,9  

To form smallest number with the given digits ,the smaller digit is repeated.

In the given digits, the smaller number is ‘3’, which is to be repeated.

Step-1: The number of digits given = 5.

The number to be formed is 6^th digit number, which need one more digit.

Step-2 : The Ascending order of the given digits : 3 < 4 < 7 < 8 < 9 .  

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

Lakhs    (L)	TenThousands       (TTh)	Thousands     (Th)	Hundreds     (H)	Tens   (T)	Ones   (O)
3	3	4	7	8	9

 

 

2) Digits :  3 , 1 , 8 , 0  

a) Greatest Number:

Here, the number of digits given are lesser than the digit to be formed.

So, to form greatest number with the given digits ,the greater digit is repeated.

In the given digits, the greater number is ‘ 8’, which is to be repeated.

Step-1: The number of digits given = 4.

The number to be formed is 6^th digit number, which need two more digits.

Step-2:  Descending Order of the given digits:  8 > 3 > 1 >0 .

Step – 3: The digit  8, 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.

Lakhs    (L)	TenThousands       (TTh)	Thousands     (Th)	Hundreds     (H)	Tens   (T)	Ones   (O)
8	8	8	3	1	0

 

Thus the greatest number formed is :  8,88,310 .

 

b) Smallest number:

The given digits are: 3 , 1 , 8 , 0 . 

To form smallest number with the given digits ,the smaller digit is repeated. Here, digit ‘ 0 ‘ is in the given digits. So, we need to check the next smaller number which is smaller in the given digits i.e; ‘1’.

First, digit ‘1’  has to put in greatest place value,then the digit ‘0’ is repeated three times in the next corresponding place values followed by next three digits in the next place values to form smallest 6^th digit number.

In the given digits, the smaller number is ‘0’, which is to be repeated.

Step-1: The number of digits given = 4.

The number to be formed is 6^th digit number, which need two more digits.

Step-2 : The  Ascending order of the given digits : 0 < 1 < 3  < 8 .  

Step – 3: The digit ‘1’, which is smaller need to put greatest place value . i.e; Lakhs(L) , digit ‘0’ is placed in TenThousands(TTh) ,Thousands(Th) ,Hundreds(H) , the next smaller numbers are placed in next  place values.

Lakhs    (L)	TenThousands       (TTh)	Thousands     (Th)	Hundreds     (H)	Tens   (T)	Ones   (O)
1	0	0	0	3	8

Thus, the smallest number formed is : 1,00,038.

 

The Table shows building the Greatest and Smallest 6^th digit number with the given digits:

S.NO	DIGITS	GREATEST NUMBER	SMALLEST NUMBER
1	3, 1, 4	4,44,431	1,11,134
2	8,0,3,6,4	8,86,430	3,00,468
3	9,2, 6,7	9,99,762	2,22,679

Rounding Off Whole Numbers.

ROUNDING OFF NUMBERS:

Rounding off of a number is an estimation  done to make the complex numbers simplier and also making sure that the value of the Rounded-off number remains unchanged.

                                      ( or)

Rounding means making a number simpler but keeping its value close to what it was. The result is less accurate, but easier to use.

Example: 83 rounded to the nearest ten is 80, because 83 is closer to 80 than to 90. But 86 goes up to 90.

We Round off the numbers nearer to their Tens,Hundreds,Thousands and so on.

While Rounding off a number ,we need to follow the steps.

Step-1 : Underline the  digit in the given place to be rounded in the number.

Step-2 : Circle the digit right to the underlined digit .

Step-3 : Comparision: The circled digit in the number is compared with number

              ‘ 5 ‘ always.

(i) Rounded Down : If the circled digit in the number is smaller than number

( < ) ‘5’,then the number is Rounded down.i.e; the underline digit in the given place remains the same.

(ii)  Rounded Up: If the circled digit in the number is greater than or equals to

 ( ≥) number ‘5’,then the number is Rounded up.i.e; the underlined digit in the given place is increased to number ‘1’.

i.e; we need to add number ‘1’ to the underlined digit.

Step-4: After Rounded-down and Rounded-up  , replace all the digits to the right of the given place with Zeros.

Note: If Round off to nearest place is not given, then we need to round off that number to its greatest place value by following the above steps.

  

1) Round off : 3,462 to its nearest Hundreds ?

 Answer:

Step-1: Underlining the digit in the given place ,(HUNDREDS place) to be rounded: 3,462 .

Step-2:  Circle the digit right to its place:Here, the digit '6' in the Tens place is to be circled.

Step-3: Comparing circled number, ‘6’ with number ‘5’. 6 > 5. So, it is Rounded-up  case.Hence, adding number ‘1’ to the digit to be rounded.i.e;

 4 + 1 =5 , which is to be replaced in Hundreds place.

Step-4 : Replace all the digits right to Hundred place with Zeroes.

Thus, the Rounded-off number to its nearest Hundreds place is: 3,500.

 

2) Round off : 9435 to its nearest Tens ?

Answer:

Step-1: Underlining the digit in the given place ,(TENS place) to be rounded:9,4 35 .

Step-2: Circle the digit right to its place:Here, the digit '5'  in the Ones place is to be circled.  

Step-3: Comparing circled number, ‘5’ with number ‘5’. 5 = 5. So, it is Rounded-up  case. Hence, adding number ‘1’ to the digit to be rounded. i.e;

 3 + 1 = 4 , which is to be replaced in Tens place.

Step-4 : Replace the digit right to Tens place with Zero.

Thus, the Rounded-off number to its nearest Tens place is: 9,440 .

 

3) Round off the number: 23,689

Answer:

Here, the digit in the number to be rounded is not specified. So, we need to round off the digit to its greatest place value.The greatest place value is TenThousand.Hence, the number 23,689 is rounded to its nearest TenThousands Place.

Step-1: Underlining the digit in the given place: 2 3,689 .

Step-2: Circle the digit right to the given digit. i.e: '3 ' is to be circled.

Step-3: Comparing the circled digit (Thousands place digit) with ‘5’.

 3 < 5. It is Round – down case. So, the digit to be rounded is write as it is.

Step-4: Replace all the digits right to TenThousands with Zeroes.

Thus the Rounded off number nearer to its TenThousands place :  20,000.

 

The below table shows the Round-Off numbers to its nearest   Tens(10),Hundreds(100),Thousands(1000). 

S.NO	NUMBER	ROUND OFF TO NEAREST PLACE
		10	100	1000
1	7,348	7,350	7,300	7,000
2	29,868	29,870	29,900	30,000
3	5,09,187	5,09,190	5,09,200	5,10,000
4	1,381	1,380	1,400	1,000
5	21,441	21,440	21,400	21,000