RS Aggarwal Class 6 Solutions Number System

RS Aggarwal class 6 solutions chapter 1 number system is one of the best study materials for the students of class 6. RS Aggarwal solutions have both questions and answers solved in an easy and comprehensive way. Solving the RS Agarwal solutions for class 6 will also help students to grab the concepts faster.

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Question 1:

Write the numeral for each of the following numbers:

(i) Nine thousand eighteen

(ii) Fifty-four thousand seventy-three

(iii) Three lakh two thousand five hundred six

(iv) Twenty lakh ten thousand eight

(v) Six crore five lakh fifty-seven

(vi) Two crore two lakh two thousand two hundred two

(vii) Twelve crore twelve lakh twelve thousand twelve

(viii) Fifteen crore fifty lakh twenty thousand sixty-eight

Solution:

(i) Nine thousand eighteen = 9018

(ii) Fifty-four thousand seventy-three = 54073

(iii) Three lakh two thousand five hundred six = 302506

(iv) Twenty lakh ten thousand eight = 2010008

(v) Six crore five lakh fifty-seven = 60500057

(vi) Two crore two lakh two thousand two hundred two = 20202202

(vii) Twelve crore twelve lakh twelve thousand twelve = 121212012

(viii) Fifteen crore fifty lakh twenty thousand sixty-eight = 155020068

 

Question 2:

Write each of the following numbers in words:

(i) 63,005 = Sixty-three thousand five

(ii) 7,07,075

(iii) 34,20,019

(iv) 3,05,09,012

(v) 5,10,03,604

(vi) 6,18,05,008

(vii) 19,09,09,900

(viii) 6,15,30,807

(ix) 6,60,60,060

Solution:

(i) 63,005 = Sixty-three thousand five

(ii) 7,07,075 = Seven lakh seven thousand seventy-five

(iii) 34,20,019 = Thirty-four lakh twenty thousand nineteen

(iv) 3,05,09,012 = Three crore five lakh nine thousand twelve

(v) 5,10,03,604 = Five crore ten lakh three thousand six hundred four

(vi) 6,18,05,008 = Six crore eighteen lakh five thousand eight

(vii) 19,09,09,900 = Nineteen crore nine lakh nine thousand nine hundred

(viii) 6,15,30,807 = Six crore fifteen lakh thirty thousand eight hundred seven

(ix) 6,60,60,060 = Six crore sixty lakh sixty thousand sixty

 

Question 3:

Write each of the following numbers in expanded form:

(i) 15,768

(ii) 3,08,927

(iii) 24,05,609

(iv) 5,36,18,493

(v) 6,06,06,006 

(vi) 9,10,10,510

Solution:

(i) 15,768 = (1 x 10000) + (5 x 1000) + (7 x 100) + (6 x 10) + (8 x 1)

(ii) 3,08,927 = (3 x 100000) + (8 x 1000) + (9 x 100) + (2 x 10) + (7 x 1)

(iii) 24,05,609 = (2 x 1000000) + (4 x 100000) + (5 x 1000) + (6 x 100) + (9 x 1)

(iv) 5,36,18,493 = (5 x 10000000) + (3 x 1000000) + (6 x 100000) + (1 x 10000) + (8 x 1000) + (4 x 100) + (9 x 10) + (3 x 1)

(v) 6,06,06,006 = (6 x 10000000) + (6 x 100000) + (6 x 1000) + (6 x 1)

(vi) 9,10,10,510 = (9 x 10000000) + (1 x 1000000) + (1 x 10000) + (5 x 100) + (1 x 10)

 

Question 4:

Write the corresponding numeral for each of the following:

(i) 6 x 10000 + 2 x 1000 + 5 x 100 + 8 x 10 + 4 x 1

(ii) 5 x 100000 + 8 x 10000 + 1 x 1000 + 6 x 100 + 2 x 10 + 3 x1

(iii) 2 x 10000000 + 5 x 100000 + 7 x 1000 + 9 x 100 + 5 x 1

(iv) 3 x 1000000 + 4 x 100000 + 6 x 1000 + 5 x 100 + 7 x 1

Solution:

(i) 6 x 10000 + 2 x 1000 + 5 x 100 + 8 x 10 + 4 x 1 = 62,584

(ii) 5 x 100000 + 8 x 10000 + 1 x 1000 + 6 x 100 + 2 x 10 + 3 x1 = 5,81,623

(iii) 2 x 10000000 + 5 x 100000 + 7 x 1000 + 9 x 100 + 5 x 1 = 2,05,07,905

(iv) 3 x 1000000 + 4 x 100000 + 6 x 1000 + 5 x 100 + 7 x 1 = 34,06,507

 

Question 5:

Find the difference between the place values of the two nines in 79520986.

Solution:

The place value of 9 at ten lakhs place = 90 lakhs = 9000000

The place value of 9 at hundreds places = 9 hundred = 900

Therefore, Required difference = (9000000 – 900) = 8999100

 

Question 6:

Find the difference between the place value and the face value of 7 in 27650934.

Solution:

The place value of 7 in 27650934 = 70 lakhs = 70,00,000

The face value of 7 in 27650934 = 7

Therefore, Required difference = (7000000 – 7) = 69,99,993

 

Question 7:

How many 6-digit numbers are there in all?

Solution:

The largest 6-digit number = 999999

The smallest 6-digit number = 100000

Therefore, Total number of 6-digit numbers = (999999 – 100000) + 1

= 899999 + 1

= 900000

= 9 lakhs

 

Question 8:

How many 7-digit numbers are there in all?

Solution:

The largest 7-digit number = 9999999

The smallest 7-digit number = 1000000

Therefore, Total number of 7-digit numbers = (9999999 – 1000000)

= 8999999 + 1

= 9000000

= Ninety lakhs

 

Question 9:

How many thousands make a lakh?

Solution:

One lakh (1,00,000) is equal to one hundred thousand (100 x 1000).

Thus, one hundred thousand make a lakh.

 

Question 10:

How many thousands make a crore?

Solution:

One crore (1,00,00,000) is equal to one hundred lakh (10,000 x 1,000).

Thus, 10,000 thousand make a crore.

 

Question 11:

Find the difference between the number 738 and that obtained on reversing its digits.

Solution:

The given number is 738.

On reversing the digits of this number, we get 837.

Therefore, Required difference = 837 – 738 = 99

 

Question 12:

What comes just after 9547999?

Solution:

The number just after 9547999 is 9547999 + 1 = 9548000.

 

Question 13:

What comes just before 9900000?

Solution:

The number just before 9900000 is 9900000 – 1 = 9899999.

 

Question 14:

What comes just before 10000000?

Solution:

The number just before 10000000 is 10000000 – 1 = 9999999.

 

Question 15:

Write all 3-digit numbers using 2, 3, 4, taking each digit only once.

Solution:

The 3-digit numbers formed by 2, 3 and 4 by taking each digit only once are 234, 324, 243, 342, 423 and 432.

 

Question 16:

Write the smallest number of different digits formed by using the digits 3, 1, 0, 5 and 7.

Solution:

The smallest number formed by using each of the given digits (i.e., 3, 1, 0, 5 and 7) only once is 10357.

 

Question 17:

Write the largest number of different digits formed by using the digits 2, 4, 0, 3, 6 and 9.

Solution:

The largest number formed by using each of the given digits only once is 964320.

 

Question 18:

Rewrite each of the following numerals with proper commas, using the international place-value chart. Also, write the number name of each in the international system.

(i) 735821

(ii) 6057894

(iii) 56943821

(iv) 37502093

(v) 89350064

(vi) 90703006

Solution:

Representation of the numbers on the international place-value chart:

PeriodsMillionsThousandsOnesPlaceHundred millionsTen millionsMillionsHundred thousandsTen thousandsThousandsHundredsTensOnesHMTMMH ThT ThThHTO(i)

735821(ii)

6057894(iii)
56943821(iv)
37502093(v)
89350064(vi)
90703006

CroreTen lakhsLakhsTen ThousandThousandHundredTensOnes

 

The number names of the given numbers in the international system:

(i) 735,821 = Seven hundred thirty-five thousand eight hundred twenty-one

(ii) 6,057,894 = Six million fifty-seven thousand eight hundred ninety-four

(iii) 56,943,821 = Fifty-six million nine hundred forty-three thousand eight hundred twenty-one

(iv) 37,502,093 = Thirty-seven million five hundred two thousand ninety-three

(v) 89,350,064 = Eighty-nine million three hundred fifty thousand sixty-four

(vi) 90,703,006 = Ninety million seven hundred three thousand and six

 

Question 19:

Write each of the following in figures in the international place-value chart:

(i) Thirty million one hundred five thousand sixty-three

(ii) Fifty-two million two hundred five thousand six

(iii) Five million five thousand five

Solution:

PeriodsMillionsThousandsOnesPlaceHundred millionsTen millionsMillionsHundred thousandsTen thousandsThousandsHundredsTensOnesHMTMMH ThT ThThHTO(i)
30105063(ii)
52205006(iii)

5005005

Exercise 1B

Fill in each of the following boxes with the correct symbol > or < :

Question 1:

1003467 ___987965

Solution:

1003467 > 987965

We know that a 7-digit number is always greater than a 6-digit number. Since 1003467 is a 7-digit number and 987965 is a 6-digit number, 1003467 is greater than 987965.

 

Question 2:

3572014 ___10235401

Solution:

3572014 < 10235401

We know that a 7-digit number is always less than an 8-digit number. Since 3572014 is a 7-digit number and 10235401 is an 8-digit number, 3572014 is less than 10235401.

 

Question 3:

3254790 ___3260152

Solution:

Both the numbers have the digit 3 at the ten lakhs places.

Also, both the numbers have the digit 2 at the lakhs places.

However, the digits at the ten thousands place in 3254790 and 3260152 are 5 and 6, respectively.

Clearly, 5 < 6

Therefore, 3254790 < 3260152

 

Question 4:

10357690 ___11243567

Solution:

Both have the digit 1 at the crores places.

However, the digits at the ten lakhs places in 10357690 and 11243567 are 0 and 1, respectively.

Clearly, 0 < 1

Therefore, 10357690 < 11243567

 

Question 5:

27596381 ___7965412

Solution:

27596381 > 7965412

We know that an 8-digit number is always greater than a 7-digit number. Since 7965412 is a 7-digit number and 27596381 is an 8-digit number, 27596381 is greater than 7965412.

 

Question 6:

47893501 ___47894021

Solution:

Both the numbers have the same digits, namely 4, 7, 8 and 9, at the crores, ten lakhs, lakhs and ten thousand places, repectively.

However, the digits at the thousands place in 47893501 and 47894021 are 3 and 4, respectively.

Clearly, 3 < 4

Therefore, 47893501 < 47894021

Arrange the following numbers in descending order:

Question 7:

63521047, 7354206, 63514759, 7355014, 102345680

Solution:

102345680 is a 9-digit number.

63521047 and 63514759 are both 8-digit numbers.

Both the numbers have the same digits, namely 6, 3 and 5, at the crores, ten lakhs and lakhs places, respectively.

However, the digits at the ten thousand place in 63521047 and 63514759 are 2 and 1, respectively.

Clearly 2 > 1

Therefore, 63521047 > 63514759

7355014 and 7354206 are both 7-digit numbers.

Both the numbers have the same digits, namely 7, 3 and 5 at the crores, ten lakhs and lakhs places, respectively.

However, the digits at the ten thousand place in 7355014 and 7354206 are 5 and 4, respectively.

Clearly, 5 > 4

Therefore, 7355014 > 7354206

The given numbers in descending order are:

1023456080 > 63521047 > 63514759 > 7355014 > 7354206

 

Question 8:

5032786, 23794206, 5032790, 23756819, 987876

Solution:

23794206 and 23756819 are both 8-digit numbers.

Both the numbers have the same digits, namely 2, 3 and 7 at the crores, ten lakhs and lakhs places, respectively.

However, the digits at the ten thousand place in 23794206 and 23756819 are 9 and 5, respectively.

Clearly, 9 > 5

Therefore, 23794206 > 23756819

5032790 and 5032786 are both 7-digit numbers.

Both the numbers have the same digits, namely 5, 0, 3, 2 and 7, at the ten lakhs, lakhs, ten thousand, thousands and hundreds place, respectively.

However, the digits at the tens place 5032790 and 5032786 are 9 and 8, respectively.

Clearly, 9 > 8

Therefore, 5032790 > 5032786

987876 is a 6-digit number.

The given numbers in descending order are:

23794206 > 23756819 > 5032790 > 5032786 > 987876

 

Question 9:

19090, 1808088, 16060666, 16007777, 181888, 1808090

Solution:

16060666 and 16007777 are both 8-digit numbers.

Both the numbers have the same digits, namely 1, 6 and 0, at the crores, ten lakhs and lakhs places, respectively.

However, the digits at the ten thousands place is 16060666 and 16007777 are 6 and 0, respectively.

Clearly, 6 > 0

Therefore, 16060666 > 16007777

1808090 and 1808088 are both 7-digit numbers.

Both the numbers have the same digits, namely 1, 8, 0, 8 and 0, at ten lakhs, ten thousands, thousands and hundred places, respectively.

However, the digits at the tens place in 1808090 and 1808088 are 9 and 8, respectively.

Clearly, 9 > 8

Therefore, 1808090 > 1808088

190909 and 181888 are both 6-digit numbers.

Both the numbers have the same digit, 1, at the lakhs place.

However, the digits at the ten thousands place in 190909 and 181888 are 9 and 8, respectively.

Clearly, 9 > 8

Therefore, 190909 > 181888

Thus, the given numbers in descending order are:

16060666 > 16007777 > 1808090 > 1808088 > 190909 > 181888

 

Question 10:

199988, 1704382, 200175, 1702497, 201200, 1712040

Solution:

1712040, 1704382 and 1702497 are all 7-digit numbers.

The three numbers have the same digits, namely 1 and 7, at ten lakhs and lakhs places, respectively.

However, the digits at the ten thousands place in 1712040, 1704382 and 1702497 are 1, 0 and 0.

Therefore, 1712040 is the largest.

Of the other two numbers, the respective digits at the thousands places are 4 and 2.

Clearly, 4 > 2

Therefore, 1704382 > 1702497

201200, 200175 and 199988 are all 6-digit numbers.

At the lakhs place, we have 2 > 1.

So, 199988 is the smallest of the three numbers.

The other two numbers have the same digits, namely 2 and 0, at the lakhs and ten thousands places, respectively.

However, the digits at the thousands place in 201200 and 200175 are 1 and 0, respectively.

Clearly, 1 > 0

Therefore, 201200 > 200175

The given numbers in descending order are:

1712040 > 1704382 > 1702497 > 201200 > 200175 > 199988

Arrange the following numbers in ascending order:

 

Question 11:

9873426, 24615019, 990357, 9874012, 24620010

Solution:

990357 is a 6-digit number.

9873426 and 9874012 are both 7-digit numbers.

Both the numbers have the same digits, namely 9, 8 and 7, at the ten lakhs, lakhs and ten thousands places, respectively.

However, the digits at the thousands place in 9873426 and 9874012 are 3 and 4, respectively.

Clearly, 4 < 7

Therefore, 9873426 < 9874012

24615019 and 24620010 are both 8-digit numbers.

Both the numbers have the same digits, namely 2, 4 and 6, at the crores, ten lakhs and lakhs places, respectively.

However, the digits at the ten thousands place in 24615019 and 24620010 are 2 and 1, respectively.

Clearly, 1 < 2

Therefore, 24615019 < 24620010

The given numbers in ascending order are:

990357 < 9873426 < 9874012 < 24615019 < 24620010

 

Question 12:

56943201, 5694437, 56944000, 5695440, 56943300

Solution:

5694437 and 5695440 are both 7-digit numbers.

Both have the same digit, i.e., 5 at the ten lakhs place.

Both have the same digit, i.e., 6 at the lakhs place.

Both have the same digit, i.e., 9 at the ten thousand place.

However, the digits at the thousand place in 5694437 and 5695440 are 4 and 5, respectively.

Clearly, 4 < 5

Therefore, 5694437 < 5695440

56943201, 56943300 and 56944000 are all 8-digit numbers.

They have the same digit, i.e., 5 at the crores place.

They have the same digit, i.e., 6 at the ten lakhs place.

They have the same digit, i.e., 9 at the lakhs place.

They have the same digit, i.e., 5 at the ten thousands place.

However, at the thousands place, one number has 4 while the others have 3.

Therefore, 56944000 is the largest.

The other two numbers have 3 and 2 at their hundreds places.

Clearly, 2 < 3

Therefore, 56943201 < 56943300

The given numbers in ascending order are:

5694437 < 5695440 < 56943201 < 56943300 < 56944000

 

Question 13:

700087,8014257, 8015032, 10012458, 8014306

Solution:

700087 is 6-digit number.

8014257, 8014306 and 8015032 are all 7-digit numbers.

They have the same digits, namely 8, 0 and 1, at the ten lakhs, lakhs and ten thousand places, respectively.

But, at the thousands place, one number has 5 while the other two numbers have 4.

Here, 801503 is the largest.

The other two numbers have 2 and 3 at their hundreds of places.

Clearly, 2 < 3

Therefore, 8014306 < 8015032

10012458 is an 8-digit number.

The given numbers in ascending order are:

700087 < 8014257 < 8014306 < 8015032 < 10012458

 

Question 14:

1020304, 893245, 980134, 1021403, 893425, 1020216

Solution:

893245, 893425 and 980134 are all 6-digit numbers.

Among the three, 980134 is the largest.

The other two numbers have the same digits, namely 8, 9 and 3, at the lakhs, ten thousand and thousands of places, respectively.

However, the digits at the hundreds place in 893245 and 893425 ae 2 and 4, respectively.

Clearly, 2 < 4

Therefore, 893245 < 893425

1020216, 1020304 and 1021403 are all 7-digit numbers.

They have the same digits, namely 1, 0 and 2, at the ten lakhs, lakhs and ten thousand places, respectively.

At the thousands place, 1021403 has 1.

The other two numbers have the digits 2 and 3 at their hundred places.

Clearly, 2 < 3

Therefore, 1020216 < 1020304

The given numbers in ascending order are:

893245 < 893425 < 980134 < 1020216 < 1020304 < 1021403


Practise This Question

If x3=9, then x is equal to