#### Chapters

## Chapter 1: Number System

### NCERT solutions for Mathematics Exemplar Class 6 Chapter 1 Number System Exercise [Pages 5 - 20]

#### Choose the correct alternative:

The product of the place values of two 2’s in 428721 is ______.

4

40000

400000

40000000

3 × 10000 + 7 × 1000 + 9 × 100 + 0 × 10 + 4 is the same as ______.

3794

37940

37904

379409

If 1 is added to the greatest 7-digit number, it will be equal to ______.

10 thousand

1 lakh

10 lakh

1 crore

The expanded form of the number 9578 is ______.

9 × 10000 + 5 × 1000 + 7 × 10 + 8 × 1

9 × 1000 + 5 × 100 + 7 × 10 + 8 × 1

9 × 1000 + 57 × 10 + 8 × 1

9 × 100 + 5 × 100 + 7 × 10 + 8 × 1

When rounded off to nearest thousands, the number 85642 is ______.

85600

85700

85000

86000

The largest 4-digit number, using any one digit twice, from digits 5, 9, 2 and 6 is ______.

9652

9562

9659

9965

In Indian System of Numeration, the number 58695376 is written as ______.

58, 69, 53, 76

58, 695, 376

5, 86, 95, 376

586, 95, 376

One million is equal to ______.

1 lakh

10 lakh

1 crore

10 crore

The greatest number which on rounding off to nearest thousands gives 5000, is ______.

5001

5559

5999

5499

Keeping the place of 6 in the number 6350947 same, the smallest number obtained by rearranging other digits is ______.

6975430

6043579

6034579

6034759

Which of the following numbers in Roman numerals is incorrect?

LXXX

LXX

LX

LLX

The largest 5-digit number having three different digits is ______.

98978

99897

99987

98799

The smallest 4-digit number having three different digits is ______.

1102

1012

1020

1002

Number of whole numbers between 38 and 68 is ______.

31

30

29

28

The product of successor and predecessor of 999 is ______.

999000

998000

989000

1998

The product of a non-zero whole number and its successor is always ______.

An even number

An odd number

A prime number

Divisible by 3

A whole number is added to 25 and the same number is subtracted from 25. The sum of the resulting numbers is ______.

0

25

50

75

Which of the following is not true?

(7 + 8) + 9 = 7 + (8 + 9)

(7 × 8) × 9 = 7 × (8 × 9)

7 + 8 × 9 = (7 + 8) × (7 + 9)

7 × (8 + 9) = (7 × 8) + (7 × 9)

By using dot (.) patterns, which of the following numbers can be arranged in all the three ways namely a line, a triangle and a rectangle?

9

10

11

12

Which of the following statements is not true?

Both addition and multiplication are associative for whole numbers.

Zero is the identity for multiplication of whole numbers.

Addition and multiplication both are commutative for whole numbers.

Multiplication is distributive over addition for whole numbers.

Which of the following statements is not true?

0 + 0 = 0

0 – 0 = 0

0 × 0 = 0

0 ÷ 0 = 0

The predecessor of 1 lakh is ______.

99000

99999

999999

100001

The successor of 1 million is ______.

2 millions

1000001

100001

10001

Number of even numbers between 58 and 80 is ______.

10

11

12

13

Sum of the number of primes between 16 to 80 and 90 to 100 is ______.

20

18

17

16

Which of the following statements is not true?

The HCF of two distinct prime numbers is 1

The HCF of two co-prime numbers is 1

The HCF of two consecutive even numbers is 2

The HCF of an even and an odd number is even

The number of distinct prime factors of the largest 4-digit number is ______.

2

3

5

11

The number of distinct prime factors of the smallest 5-digit number is ______.

2

4

6

8

If the number 7254 * 98 is divisible by 22, the digit at * is ______.

1

2

6

0

The largest number which always divides the sum of any pair of consecutive odd numbers is ______.

2

4

6

8

A number is divisible by 5 and 6. It may not be divisible by ______.

10

15

30

60

The sum of the prime factors of 1729 is ______.

13

19

32

39

The greatest number which always divides the product of the predecessor and successor of an odd natural number other than 1, is ______.

6

4

16

8

The number of common prime factors of 75, 60, 105 is ______.

2

3

4

5

Which of the following pairs is not coprime?

8, 10

11, 12

1, 3

31, 33

Which of the following numbers is divisible by 11?

1011011

1111111

22222222

3333333

LCM of 10, 15 and 20 is ______.

30

60

90

180

LCM of two numbers is 180. Then which of the following is not the HCF of the numbers?

45

60

75

90

#### State whether the following statement is True or False:

In Roman numeration, a symbol is not repeated more than three times.

True

False

In Roman numeration, if a symbol is repeated, its value is multiplied as many times as it occurs.

True

False

5555 = 5 × 1000 + 5 × 100 + 5 × 10 + 5 × 1

True

False

39746 = 3 × 10000 + 9 × 1000 + 7 × 100 + 4 × 10 + 6

True

False

82546 = 8 × 1000 + 2 × 1000 + 5 × 100 + 4 × 10 + 6

True

False

532235 = 5 × 100000 + 3 × 10000 + 2 × 1000 + 2 × 100 + 3 × 10 + 5

True

False

XXIX = 31

True

False

LXXIV = 74

True

False

The number LIV is greater than LVI.

True

False

The numbers 4578, 4587, 5478, 5487 are in descending order.

True

False

The number 85764 rounded off to nearest hundreds is written as 85700.

True

False

Estimated sum of 7826 and 12469 rounded off to hundreds is 20,000.

True

False

The largest six-digit telephone number that can be formed by using digits 5, 3, 4, 7, 0, 8 only once is 875403.

True

False

The number 81652318 will be read as eighty one crore six lakh fifty two thousand three hundred eighteen.

True

False

The largest 4-digit number formed by the digits 6, 7, 0, 9 using each digit only once is 9760.

True

False

Among kilo, milli and centi, the smallest is centi.

True

False

Successor of a one digit number is always a one digit number.

True

False

Successor of a 3-digit number is always a 3-digit number.

True

False

Predecessor of a two-digit number is always a two digit number.

True

False

Every whole number has its successor.

True

False

Every whole number has its predecessor.

True

False

Between any two natural numbers, there is one natural number.

True

False

The smallest 4-digit number is the successor of the largest 3-digit number.

True

False

Of the given two natural numbers, the one having more digits is greater.

True

False

Natural numbers are closed under addition.

True

False

Natural numbers are not closed under multiplication.

True

False

Natural numbers are closed under subtraction.

True

False

Addition is commutative for natural numbers.

True

False

1 is the identity for addition of whole numbers.

True

False

1 is the identity for multiplication of whole numbers

True

False

There is a whole number which when added to a whole number, gives the number itself.

True

False

There is a natural number which when added to a natural number, gives the number itself.

True

False

If a whole number is divided by another whole number, which is greater than the first one, the quotient is not equal to zero.

True

False

Any non-zero whole number divided by itself gives the quotient 1.

True

False

The product of two whole numbers need not be a whole number.

True

False

A whole number divided by another whole number greater than 1 never gives the quotient equal to the former.

True

False

Every multiple of a number is greater than or equal to the number.

True

False

The number of multiples of a given number is finite.

True

False

Every number is a multiple of itself.

True

False

Sum of two consecutive odd numbers is always divisible by 4.

True

False

If a number divides three numbers exactly, it must divide their sum exactly.

True

False

If a number exactly divides the sum of three numbers, it must exactly divide the numbers separately.

True

False

If a number is divisible both by 2 and 3, then it is divisible by 12.

True

False

A number with three or more digits is divisible by 6, if the number formed by its last two digits (i.e., ones and tens) is divisible by 6.

True

False

A number with 4 or more digits is divisible by 8, if the number formed by the last three digits is divisible by 8.

True

False

If the sum of the digits of a number is divisible by 3, then the number itself is divisible by 9.

True

False

All numbers which are divisible by 4 may not be divisible by 8

True

False

The Highest Common Factor of two or more numbers is greater than their Lowest Common Multiple.

True

False

LCM of two or more numbers is divisible by their HCF.

True

False

LCM of two numbers is 28 and their HCF is 8.

True

False

LCM of two or more numbers may be one of the numbers.

True

False

HCF of two or more numbers may be one of the numbers.

True

False

Every whole number is the successor of another whole number.

True

False

Sum of two whole numbers is always less than their product.

True

False

If the sum of two distinct whole numbers is odd, then their difference also must be odd.

True

False

Any two consecutive numbers are coprime.

True

False

If the HCF of two numbers is one of the numbers, then their LCM is the other number.

True

False

The HCF of two numbers is smaller than the smaller of the numbers.

True

False

The LCM of two numbers is greater than the larger of the numbers.

True

False

The LCM of two coprime numbers is equal to the product of the numbers.

True

False

#### Fill in the blank:

10 million = ______ crore.

10 lakh = _____ million.

1 metre = _____ millimetres.

1 centimetre = _____ millimetres.

1 kilometre = _____ millimetres.

1 gram = _____ milligrams.

1 litre = _____ millilitres.

1 kilogram = _____ miligrams.

100 thousands = _____ lakh.

Height of a person is 1 m 65 cm. His height in millimetres is ______.

Length of river ‘Narmada’ is about 1290 km. Its length in metres is ______.

The distance between Sringar and Leh is 422 km. The same distance in metres is ______.

Writing of numbers from the greatest to the smallest is called an arrangement in _____ order.

By reversing the order of digits of the greatest number made by five different non-zero digits, the new number is the _____ number of five digits.

By adding 1 to the greatest _____ digit number, we get ten lakh.

The number five crore twenty-three lakh seventy-eight thousand four hundred one can be written, using commas, in the Indian System of Numeration as ______.

In Roman Numeration, the symbol X can be subtracted from _____, M and C only. 111. The number 66

The number 66 in Roman numerals is ______.

The population of Pune was 2,538,473 in 2001. Rounded off to nearest thousands, the population was ______.

The smallest whole number is ______.

Successor of 106159 is ______.

Predecessor of 100000 is ______.

400 is the predecessor of ______.

______ is the successor of the largest 3 digit number.

If 0 is subtracted from a whole number, then the result is the _____ itself .

The smallest 6 digit natural number ending in 5 is ______.

Whole numbers are closed under _____ and under _____.

Natural numbers are closed under _____ and under _____.

Division of a whole number by _____ is not defined.

Multiplication is distributive over _____ for whole numbers.

2395 × _____ = 6195 × 2395

1001 × 2002 = 1001 × (1001 + _____ )

10001 × 0 = ______.

2916 × _____ = 0

9128 × _____ = 9128

125 + (68 + 17) = (125 + _____ ) + 17

8925 × 1 = ______.

19 × 12 + 19 = 19 × (12 + _____)

24 × 35 = 24 × 18 + 24 × _____.

32 × (27 × 19) = (32 × _____ ) × 19

786 × 3 + 786 × 7 = ______.

24 × 25 = 24 × ______.

A number is a _____ of each of its factor.

______ is a factor of every number.

The number of factors of a prime number is ______.

A number for which the sum of all its factors is equal to twice the number is called a _____ number.

The numbers having more than two factors are called _____ numbers.

2 is the only _____ number which is even.

Two numbers having only 1 as a common factor are called _____ numbers.

Number of primes between 1 to 100 is ______.

If a number has _____ in ones place, then it is divisible by 10.

A number is divisible by 5, if it has _____ or _____ in its ones place.

A number is divisible by _____ if it has any of the digits 0, 2, 4, 6, or 8 in its ones place.

If the sum of the digits in a number is a _____ of 3, then the number is divisible by 3.

If the difference between the sum of digits at odd places (from the right) and the sum of digits at even places (from the right) of a number is either 0 or divisible by _____, then the number is divisible by 11.

The LCM of two or more given numbers is the lowest of their common ______.

The HCF of two or more given numbers is the highest of their common _____.

#### Match the Column:

Column I |
Column II |

(i) The difference of two consecutive whole numbers |
(a) odd |

(ii) The product of two non-zero consecutive whole numbers |
(b) 0 |

(iii) Quotient when zero is divided by another non-zero whole number |
(c) 3 |

(iv) 2 added three times, to the smallest whole number |
(d) 1 |

(v) Smallest odd prime number | (e) 6 |

(f) even |

Arrange the followng numbers in descending order:

8435, 4835, 13584, 5348, 25843

Of the following numbers which is the greatest? Which is the smallest 38051425, 30040700, 67205602

Write in expanded form:

74836

Write in expanded form:

574021

Write in expanded form:

8907010

As per the census of 2001, the population of four states are given below. Arrange the states in ascending and descending order of their population.

(a) Maharashtra | 96878627 |

(b) Andhra Pradesh | 76210007 |

(c) Bihar | 82998509 |

(d) Uttar Pradesh | 166197921 |

The diameter of Jupiter is 142800000 metres. Insert commas suitably and write the diameter according to International System of Numeration.

India’s population has been steadily increasing from 439 millions in 1961 to 1028 millions in 2001. Find the total increase in population from 1961 to 2001. Write the increase in population in Indian System of Numeration, using commas suitably.

Radius of the Earth is 6400 km and that of Mars is 4300000 m. Whose radius is bigger and by how much?

In 2001, the poplulations of Tripura and Meghalaya were 3,199,203 and 2,318,822, respectively. Write the populations of these two states in words.

In a city, polio drops were given to 2,12,583 children on Sunday in March 2008 and to 2,16,813 children in the next month. Find the difference of the number of children getting polio drops in the two months

A person had Rs 1000000 with him. He purchased a colour T.V. for Rs 16580, a motor cycle for Rs 45890 and a flat for Rs 870000. How much money was left with him?

Out of 180000 tablets of Vitamin A, 18734 are distributed among the students in a district. Find the number of the remaining vitamin tablets.

Chinmay had Rs 610000. He gave Rs 87500 to Jyoti, Rs 126380 to Javed and Rs 350000 to John. How much money was left with him?

Find the difference between the largest number of seven digits and the smallest number of eight digits.

A mobile number consists of ten digits. The first four digits of the number are 9, 9, 8 and 7. The last three digits are 3, 5 and 5. The remaining digits are distinct and make the mobile number, the greatest possible number. What are these digits?

A mobile number consists of ten digits. First four digits are 9,9,7 and 9. Make the smallest mobile number by using only one digit twice from 8, 3, 5, 6, 0

In a five digit number, digit at ten’s place is 4, digit at unit’s place is one fourth of ten’s place digit, digit at hunderd’s place is 0, digit at thousand’s place is 5 times of the digit at unit’s place and ten thousand’s place digit is double the digit at ten’s place. Write the number.

Find the sum of the greatest and the least six digit numbers formed by the digits 2, 0, 4, 7, 6, 5 using each digit only once.

A factory has a container filled with 35874 litres of cold drink. In how many bottles of 200 ml capacity each can it be filled?

The population of a town is 450772. In a survey, it was reported that one out of every 14 persons is illiterate. In all how many illiterate persons are there in the town?

Find the LCM of 80, 96, 125, 160.

Make the greatest and the smallest 5-digit numbers using different digits in which 5 appears at ten’s place.

How many grams should be added to 2 kg 300 g to make it 5 kg 68 g?

A box contains 50 packets of biscuits each weighing 120 g. How many such boxes can be loaded in a van which cannot carry beyond 900 kg?

How many lakhs make five billions?

How many millions make 3 crores?

Estimate the following by rounding off number to nearest hundreds:

874 + 478

Estimate the following by rounding off number to nearest hundreds:

793 + 397

Estimate the following by rounding off number to nearest hundreds:

11244 + 3507

Estimate the following by rounding off number to nearest hundreds:

17677 + 13589

Estimate the follwoing by rounding off number to nearest tens:

11963 – 9369

Estimate the following by rounding off number to nearest tens:

76877 – 7783

Estimate the following by rounding off number to nearest tens:

10732 – 4354

Estimate the following by rounding off number to nearest tens:

78203 – 16407

Estimate the following products by rounding number to nearest tens:

87 × 32

Estimate the following products by rounding number to nearest tens:

311 × 113

Estimate the following products by rounding number to nearest tens:

3239 × 28

Estimate the following products by rounding number to nearest tens:

3239 × 28

The population of a town was 78787 in the year 1991 and 95833 in the year 2001. Estimate the increase in population by rounding off each population to nearest hundreds.

Estimate the product 758 × 6784 using the general rule.

A garment factory produced 216315 shirts, 182736 trousers and 58704 jackets in a year. What is the total production of all the three items in that year?

Find the LCM of 160, 170 and 90

A vessel has 13 litres 200 mL of fruit juice. In how many glasses each of capacity 60 mL can it be filled?

Determine the sum of the four numbers as given below:

Successor of 32

Determine the sum of the four numbers as given below:

Predecessor of 49

Determine the sum of the four numbers as given below:

Predecessor of the predecessor of 56

Determine the sum of the four numbers as given below:

Successor of successor of 67

A loading tempo can carry 482 boxes of biscuits weighing 15 kg each, whereas a van can carry 518 boxes each of the same weight. Find the total weight that can be carried by both the vehicles.

In the marriage of her daughter, Leela spent Rs 216766 on food and decoration, Rs 122322 on jewellery, Rs 88234 on furniture and Rs 26780 on kitchen items. Find the total amount spent by her on the above items.

A box contains 5 strips having 12 capsules of 500mg medicine in each capsule. Find the total weight in grams of medicine in 32 such boxes.

Determine the least number which when divided by 3, 4 and 5 leaves remainder 2 in each case.

A merchant has 120 litres of oil of one kind, 180 litres of another kind and 240 litres of a third kind. He wants to sell the oil by filling the three kinds of oil in tins of equal capacity. What should be the greatest capacity of such a tin?

Find a 4-digit odd number using each of the digits 1, 2, 4 and 5 only once such that when the first and the last digits are interchanged, it is divisible by 4.

Using each of the digits 1, 2, 3 and 4 only once, determine the smallest 4-digit number divisible by 4.

Fatima wants to mail three parcels to three village schools. She finds that the postal charges are Rs 20, Rs 28 and Rs 36, respectively. If she wants to buy stamps only of one denomination, what is the greatest denomination of stamps she must buy to mail the three parcels?

Three brands A, B and C of biscuits are available in packets of 12, 15 and 21 biscuits respectively. If a shopkeepeer wants to buy an equal number of biscuits, of each brand, what is the minimum number of packets of each brand, he should buy?

The floor of a room is 8 m 96 cm long and 6 m 72 cm broad. Find the minimum number of square tiles of the same size needed to cover the entire floor.

In a school library, there are 780 books of English and 364 books of Science. Ms. Yakang, the librarian of the school wants to store these books in shelves such that each shelf should have the same number of books of each subject. What should be the minimum number of books in each shelf?

In a colony of 100 blocks of flats numbering 1 to 100, a school van stops at every sixth block while a school bus stops at every tenth block. On which stops will both of them stop if they start from the entrance of the colony?

Test the divisibility of following numbers by 11

5335

Test the divisibility of following numbers by 11

9020814

Using divisibility tests, determine which of the following numbers are divisible by 4?

4096

Using divisibility tests, determine which of the following numbers are divisible by 4?

21084

Using divisibility tests, determine which of the following numbers are divisible by 4?

31795012

Using divisibility test, determine which of the following numbers are divisible by 9?

672

Using divisibility test, determine which of the following numbers are divisible by 9?

5652

## Chapter 1: Number System

## NCERT solutions for Mathematics Exemplar Class 6 chapter 1 - Number System

NCERT solutions for Mathematics Exemplar Class 6 chapter 1 (Number System) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics Exemplar Class 6 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Mathematics Exemplar Class 6 chapter 1 Number System are Introduction to Knowing Our Numbers, Comparing Numbers, Compare Numbers in Ascending and Descending Order, Compare Number by Forming Numbers from a Given Digits, Compare Numbers by Shifting Digits, Introducing a 5 Digit Number - 10,000, Revisiting Place Value of Numbers, Expansion Form of Numbers, Introducing the Six Digit Number - 1,00,000, Larger Number of Digits 7 and Above, An Aid in Reading and Writing Large Numbers, Using Commas in Indian and International Number System, Round off and Estimation of Numbers, To Estimate Sum Or Difference, Estimating Products of Numbers, Simplification of Expression by Using Brackets, BODMAS - Rules for Simplifying an Expression, Roman Numbers System and Its Application, Concept for Natural Numbers, Concept for Whole Numbers, Successor and Predecessor of Whole Number, Operation of Whole Numbers on Number Line, Properties of Whole Numbers, Closure Property of Whole Number, Associativity Property of Whole Numbers, Division by Zero, Commutativity Property of Whole Number, Distributivity Property of Whole Numbers, Identity of Addition and Multiplication of Whole Numbers, Patterns in Whole Numbers, Arranging the Objects in Rows and Columns, Factors and Multiples, Concept of Perfect Number, Concept of Prime Numbers, Concept of Co-prime Number, Concept of Twin Prime Numbers, Concept of Even and Odd Number, Concept of Composite Number, Concept of Sieve of Eratosthenes, Tests for Divisibility of Numbers, Divisibility by 10, Divisibility by 5, Divisibility by 2, Divisibility by 3, Divisibility by 6, Divisibility by 4, Divisibility by 8, Divisibility by 9, Divisibility by 11, Common Factor, Common Multiples, Some More Divisibility Rules, Prime Factorisation, Highest Common Factor, Lowest Common Multiple.

Using NCERT Class 6 solutions Number System exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 6 prefer NCERT Textbook Solutions to score more in exam.

Get the free view of chapter 1 Number System Class 6 extra questions for Mathematics Exemplar Class 6 and can use Shaalaa.com to keep it handy for your exam preparation