NCERT Solutions for class 7 Maths Chapter 13: Exponents and Powers

Exercise 13.1

1. Find the value of:

(i) 26

Answer: 64

Explanation: 26 can be represented as:

2 × 2 × 2 × 2 × 2 × 2

= 64

(ii) 93

Answer: 729

Explanation: 93 can be represented as:

9 × 9 × 9

= 81 × 9

= 729

(iii) 112

Answer: 121

Explanation: 112 can be represented as:

11 × 11

= 121

(iv) 54

Answer: 625

Explanation: 54 can be represented as:

5 × 5 × 5 × 5

= 25 × 25

= 625

2. Express the following in exponential form:

(i) 6 × 6 × 6 × 6

Answer: 64

Explanation: The number 6 is repeated four times.

Hence, it can be represented as:

64

(ii) t × t

Answer: t2

Explanation: The variable t is repeated two times.

Hence, it can be represented as:

t2

(iii) b × b × b × b

Answer: b4

Explanation: The variable b is repeated two times.

Hence, it can be represented as:

b4

(iv) 5 × 5 × 7 × 7 × 7

Answer: 52 × 73

Explanation: The above expression has two numbers 5 and 7.

The number 5 is repeated two times and the number 7 is repeated three times.

Hence, it can be represented as:

52 × 73

(v) 2 × 2 × a × a

Answer: 22 × a2

Explanation: The above expression has one number 2 and one variable a.

The number 2 is repeated two times and the variable 'a' is also repeated two times.

Hence, it can be represented as:

22 × a2

(vi) a × a × a × c × c × c × c × d

Answer: a3 × c4 × d

Explanation: The above expression has three variables a, c, and d.

The variable 'a' is repeated three times, variable 'c' four times, and the variable 'd 'one time.

Hence, it can be represented as:

a3 × c4 × d

3. Express each of the following numbers using exponential notations:

(i) 512

Answer: 29

Explanation: 512 can be represented as:

= 2 × 256

= 2 × 2 × 128

= 2 × 2 × 2 × 64

= 2 × 2 × 2 × 2 × 32

= 2 × 2 × 2 × 2 × 2 × 16

= 2 × 2 × 2 × 2 × 2 × 2 × 8

= 2 × 2 × 2 × 2 × 2 × 2 × 2 × 4

= 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

The number 2 is repeated nine times. Hence, it can be written as:

= 29

(ii) 343

Answer: 73

Explanation: 343 can be represented as:

= 7 × 49

= 7 × 7 × 7

The number 7 is repeated three times. Hence, it can be written as:

= 73

(iii) 729

Answer: 36

Explanation: 729 can be represented as:

= 3 × 243

= 3 × 3 × 81

= 3 × 3 × 3 × 27

= 3 × 3 × 3 × 3 × 9

= 3 × 3 × 3 × 3 × 3 × 3

The number 3 is repeated six times. Hence, it can be written as:

= 36

(iv) 3125

Answer: 55

Explanation: 3125 can be represented as:

= 5 × 625

= 5 × 5 × 125

= 5 × 5 × 5 × 25

= 5 × 5 × 5 × 5 × 5

The number 5 is repeated five times. Hence, it can be written as:

= 55

4. Identify the greater number, wherever possible, in each of the following?

(i) 43 or 34

Answer: 34

Explanation: 43 can be represented as:

4 × 4 × 4

= 16 × 4

= 64

34 can be represented as:

3 × 3 × 3 × 3

= 9 × 3 × 3

= 27 × 3

= 81

81 > 64

Hence, 34 is greater.

(ii) 53 or 35

Answer: 35

Explanation: 53 can be represented as:

5 × 5 × 5

= 25 × 5

= 125

35 can be represented as:

3 × 3 × 3 × 3 × 3

= 9 × 3 × 3 × 3

= 27 × 3 × 3

= 81× 3

= 243

243 > 125

Hence, 35 is greater.

(iii) 28 or 82

Answer: 28

Explanation: 28 can be represented as:

2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

= 16 × 16

= 256

82 can be represented as:

8 × 8

= 64

256 > 64

Hence, 28 is greater.

(iv) 1002 or 2100

Answer: 2100

Explanation: 2100 is greater than 1002.

(v) 210 or 102

Answer: 210

Explanation: 210 can be represented as:

2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

= 16 × 16 × 4

= 1024

102 can be represented as:

10 × 10

= 100

1024 > 100

Hence, 210 is greater.

5. Express each of the following as product of powers of their prime factors:

(i) 648

Answer: 23 × 34

Explanation: 648 can be represented as:

= 2 × 324

= 2 × 2 × 162

= 2 × 2 × 2 × 81

= 2 × 2 × 2 × 3 × 27

= 2 × 2 × 2 × 3 × 3 × 9

= 2 × 2 × 2 × 3 × 3 × 3 × 3

The number 2 is repeated three times and the number 3 is repeated four times.

Hence, it can be written as:

23 × 34

(ii) 405

Answer: 5× 34

Explanation: 405 can be represented as:

= 5× 81

= 5 × 3 × 27

= 5 × 3 × 3 × 9

= 5 × 3 × 3 × 3 × 3

The number 5 is repeated one time and the number 3 is repeated four times.

Hence, it can be written as:

51 × 34

= 5× 34

(iii) 540

Answer: 22 × 33 × 5

Explanation: 540 can be represented as:

= 2 × 270

= 2 × 27 × 10

= 2 × 3 × 3 × 3 × 2 × 5

= 22 × 33 × 5

(iv) 3,600

Answer: 24× 32 × 52

Explanation: 3600 can be represented as:

= 60 × 60

= 3 × 2 × 2 × 5 × 3 × 2 × 2 × 5

The number 3 is repeated two times, the number 2 four times, and the number 5 two times.

Hence, the expression can be written as:

24× 32 × 52

6. Simplify:

(i) 2 × 103

Answer: 2000

Explanation: 2 × 103

The number 10 is repeated three times.

= 2 × 10 × 10 × 10

= 2 × 1000

= 2000

(ii) 72 × 22

Answer: 196

Explanation: 72 × 22

= 7 × 7 × 2 × 2

= 49 × 4

= 196

(iii) 23 × 5

Answer: 40

Explanation: 23 × 5

= 2 × 2 × 2 × 5

= 8 × 5

= 40

(iv) 3 × 44

Answer: 768

Explanation: 3 × 44

= 3 × 4 × 4 × 4 × 4

= 3 × 16 × 16

= 3 × 256

= 768

(v) 0 × 102

Answer: 0

Explanation: Any number multiplied by 0, gives 0 as the result.

(vi) 52 × 33

Answer: 675

Explanation: 52 × 33

= 5 × 5 × 3 × 3 × 3

= 25 × 27

= 675

(vii) 24 × 32

Answer: 144

Explanation: 24 × 32

= 2 × 2 × 2 × 2 × 3 × 3

= 16 × 9

= 144

(viii) 32 × 104

Answer: 90000

Explanation: 32 × 104

= 3 × 3 × 10 × 10 × 10 × 10

= 9 × 10000

= 90000

7. Simplify:

(i) (- 4)3

Answer: - 64

Explanation: (- 4)3 means that the integer (- 4) is repeated three times.

= (- 4) × (- 4) × (- 4)

= 16 × (- 4)

= - 64

(ii) (-3) × (-2)3

Answer: 24

Explanation: (- 2)3 means that the integer (- 2) is repeated three times.

(-3) × (-2)3

=(-3) × (-2) × (-2) × (-2)

= 6 × (-2) × (-2)

= -12 × (-2)

= 24

(iii) (-3)2 × (-5)2

Answer: 225

Explanation: Both the integers (- 3) and (- 5) are repeated two times.

(-3)2 × (-5)2

= (-3) × (-3) × (-5) × (-5)

= 9 × (-5) × (-5)

= (-45) × (-5)

= 225

(iv) (-2)3 × (-10)3

Answer: 8000

Explanation: Both the integers (- 2) and (- 10) are repeated three times.

(-2)3 × (-10)3

= (-2) × (-2) × (-2) × (-10) × (-10) × (-10)

= (-8) × (-1000)

= 8000

8. Compare the following numbers:

(i) 2.7 × 1012 ; 1.5 × 108

Answer: 2.7 × 1012 > 1.5 × 108

Explanation:

2.7 × 1012 = 2,700,000,000,000

1.5 × 108 = 150,000,000

Hence, 2.7 × 1012 is greater.

2.7 × 1012 > 1.5 × 108

(ii) 4 × 1014 ; 3 × 1017

Answer: 4 × 1014 < 3 × 1017

Explanation: 1017 is greater than the 1014

Hence, 4 × 1014 is greater.

3 × 1017 > 4 × 1014

Or

4 × 1014 < 3 × 1017

Exercise 13.2

1. Using laws of exponents simplify and write the answer in exponential form:

(i) 32 × 34 × 38

Answer: 312

Explanation: In the case of multiplication, the exponents are added if the base of numbers is the same.

32 × 34 × 38 = 3(2 + 4 + 8)

32 × 34 × 38 = 312

(ii) 615 ÷ 610

Answer: 65

Explanation: In the case of division, the exponents are subtracted if the base of numbers is the same.

615 ÷ 610 = 6(15 - 10)

615 ÷ 610 = 65

(iii) a3 × a2

Answer: a5

Explanation: In the case of multiplication, the exponents are added if the base of numbers is the same.

a3 × a2= a(3 + 2)

a3 × a2= a5

(iv) 7x ×72

Answer: 7(x + 2)

Explanation: In the case of multiplication, the exponents are added if the base of numbers is the same.

7x ×72 = 7(x + 2)

7x ×72 = 7x + 2

(v) (52)3 ÷ 53

Answer: 53

Explanation: The exponents in the case of double brackets are multiplied.

(52)3 = 52 x 3

(52)3 = 56

In the case of division, the exponents are subtracted if the base of numbers is the same.

56 ÷ 53 = 5(6 - 3)

56 ÷ 53 = 53

(vi) 25 × 55

Answer: 105

Explanation:

25 × 55 = (2 × 5)5

25 × 55 = (10)5

(vii) a4 × b4

Answer: (ab)4

Explanation: a4 × b4 = (a × b)4

a4 × b4 = (ab)4

a4 × b4 = ab4

(viii) (34)3

Answer: 312

Explanation: The exponents in the case of double brackets are multiplied.

(34)3 = 34 x 3

(34)3 = 312

(ix) (220 ÷ 215) × 23

Answer: 28

Explanation: (220 ÷ 215) × 23

In the case of division, the exponents are subtracted if the base of numbers is the same.

= 2(20 - 15) × 23

= 25 × 23

In the case of multiplication, the exponents are added if the base of numbers is the same.

= 2(5 + 3)

= 28

(x) 8t ÷ 82

Answer: 8t - 2

Explanation: 8t ÷ 82

In the case of division, the exponents are subtracted if the base of numbers is the same.

= 8(t - 2)

2. Simplify and express each of the following in exponential form:

(i) (23 × 34 × 4)/ (3 × 32)

Answer: 33

Explanation: To simplify, let's convert the available numbers into exponents.

4 can be written as: 2 × 2 = 22

32 can be written as: 2 × 2 × 2 × 2 × 2 = 25

Substituting the value of 4 and 32 in the expression,

(23 × 34 × 22)/ (3 × 25)

In the case of division, the exponents are subtracted, and added in the case of multiplication if the base of numbers is the same.

= (23 + 2 - 5 × 34 - 1)

= (20 × 33)

= 33

(20 = 1)

(ii) ((52)3 × 54) ÷ 57

Answer: 53

Explanation: ((52)3 × 54)÷ 57

The exponents in the case of double brackets are multiplied.

(52)3 = 52 x 3

(52)3 = 56

((52)3 × 54)÷ 57 can be written as:

(56 × 54)÷ 57

In the case of division, the exponents are subtracted, and added in the case of multiplication if the base of numbers is the same.

= (56 + 4) ÷ 57

= (510) ÷ 57

= 510 - 7

= 53

(iii) 254 ÷ 53

Answer: 55

Explanation: To simplify, let's convert the available numbers into exponents.

25 can be written as: 5 × 5 = 52

Substituting the value of 25 in the expression,

(52)4 ÷ 53

The exponents in the case of double brackets are multiplied.

(52)4 = 52 x 4

(52)4 = 58

In the case of division, the exponents are subtracted if the base of numbers is the same.

58 ÷ 53

= 58 - 3

= 55

(iv) (3 × 72 × 118)/ (21 × 113)

Answer: 7× 115

Explanation: To simplify, let's convert the available numbers into exponents.

21 can be written as: 3 × 7

Substituting the value of 21 in the expression,

(3 × 72 × 118)/ (7 × 3 × 113)

In the case of division, the exponents are subtracted, and added in the case of multiplication if the base of numbers is the same.

(31 - 1 × 72 - 1 × 118 - 3)

= (30 × 71 × 115)

= (1× 71 × 115)

= (7× 115)

(v) 37/ (34 × 33)

Answer: 30 or 1

Explanation: 37/ (34 × 33)

In the case of multiplication, the exponents are added if the base of numbers is the same.

= 37/ (34 + 3)

= 37/ 37

In the case of division, the exponents are subtracted if the base of numbers is the same.

= 37 - 7

= 30

= 1

(vi) 20 + 30 + 40

Answer: 3

Explanation: Any number with the exponent 0 is considered as 1.

20 = 1

30 = 1

40 = 1

Substituting the value in the expression, we get:

20 + 30 + 40

= 1 + 1 + 1

= 3

(vii) 20 × 30 × 40

Answer: 1

Explanation: Any number with the exponent 0 is considered as 1.

20 = 1

30 = 1

40 = 1

Substituting the value in the expression, we get:

20 × 30 × 40

= 1 × 1 × 1

= 1

(viii) (30 + 20) × 50

Answer: 2

Explanation: Any number with the exponent 0 is considered as 1.

20 = 1

30 = 1

50 = 1

Substituting the value in the expression, we get:

(30 + 20) × 50

= (1 + 1) × 1

= 2 × 1

= 2

(ix) (28 × a5)/ (43 × a3)

Answer: (2a)2

Explanation: To simplify, let's convert the available numbers into exponents.

4 can be written as: 2 × 2 = 22

Substituting the value of 4 in the expression,

(28 × a5)/ ((22)3 × a3)

(22)3 = 22 x 3

(22)3 = 26

= (28 × a5)/ (26× a3)

In the case of division, the exponents are subtracted if the base of numbers is the same.

= (28 - 6 × a5 - 3)

= (22× a2)

= (2a)2

(x) a5/a3 × a8

Answer: a10

Explanation: The above expression can be written as:

= (a5 × a8) /a3

= (a5 + 8)/a3

= a13/a3

= a10

(xi) (45 × a8b3)/(45 × a5b2)

Answer: a3b

Explanation: To simplify, let's convert the available numbers into exponents.

4 can be written as: 2 × 2 = 22

Substituting the value of 4 in the expression,

((22)5 × a8b3)/( (22)5 × a5b2)

(22)5 = 22 x 5

(22)5 = 210

(210 × a8b3)/(210 × a5b2)

In the case of division, the exponents are subtracted, and added in the case of multiplication if the base of numbers is the same.

= (210 - 10 × a8 - 5 b3 - 2)

= (20× a3b1)

= a3b

(xii) (23 × 2)2

Answer: 28

Explanation: (23 × 2)2

= 23 x 2 × 22

= 26 × 22

In the case of multiplication, the exponents are added if the base of numbers is the same.

= 26 + 2

= 28

3. Say true or false and justify your answer:

(i) 10 × 1011 = 10011

Answer: False; 10 × 1011 = 1012; 10011 = 1022

Explanation:

The expression can be written as:

10 × 1011

= 101 × 1011

In the case of multiplication, the exponents are added if the base of numbers is the same.

= 101 + 11

= 1012

Thus, the correct expression is:

10 × 1011 = 1012

10011 can be written as:

(102)11

= 102 x 11

= 1022

Thus,

10011 = 1022

(ii) 23 > 52

Answer: False; 23 < 52

Explanation: 23 can be represented as:

2 × 2 × 2 = 8

52 can be represented as:

5 × 5 = 25

8 < 25

Thus,

23 < 52

(iii) 23 × 32 = 65

Answer: False; 65 = 25 × 35

Explanation: 23 can be represented as:

2 × 2 × 2 = 8

32 can be represented as:

3 × 3 = 9

8 + 9 = 17

Thus, the given statement is incorrect.

65 can be written as 25 × 35.

65 = 25 × 35

(iv) 30 = (1000)0

Answer: True

Explanation: Any number with the exponent 0 is considered as 1.

30 = 1

10000 = 1

Hence, the given expression is true.

1 = 1

30 = (1000)0

4. Express each of the following as a product of prime factors only in exponential form:

(i) 108 × 192

Answer: 28 × 34

Explanation: 108 can be written as:

= 2 × 54

= 2 × 2 × 27

= 2 × 2 × 3 × 9

= 2 × 2 × 3 × 3 × 3

= 22 × 33

192 can be written as:

= 2 × 96

= 2 × 2 × 48

= 2 × 2 × 2 × 24

= 2 × 2 × 2 × 2 × 12

= 2 × 2 × 2 × 2 × 2 × 6

= 2 × 2 × 2 × 2 × 2 × 2 × 3

= 26 × 3

108 × 192 = (22 × 33) × (26 × 3)

In the case of multiplication, the exponents are added if the base of numbers is the same.

108 × 192 = (22 + 6 × 33 + 1)

108 × 192 = 28 × 34

(ii) 270

Answer: 33 × 5 × 2

Explanation: 270 can be written as:

= 27 × 10

= 3 × 3 × 3 × 5 × 2

= 33 × 5 × 2

(iii) 729 × 64

Answer: 36× 26

Explanation: 729 can be written as:

= 3 × 243

= 3 × 3 × 81

= 3 × 3 × 3 × 27

= 3 × 3 × 3 × 3 × 9

= 3 × 3 × 3 × 3 × 3 × 3

= 36

64 can be written as:

= 2 × 32

= 2 × 2 × 16

= 2 × 2 × 2 × 8

= 2 × 2 × 2 × 2 × 4

= 2 × 2 × 2 × 2 × 2 × 2

= 26

729 × 64 = 36× 26

(iv) 768

Answer: 28 × 3

Explanation: 768 can be written as:

= 2 × 384

= 2 × 2 × 192

= 2 × 2 × 2 × 96

= 2 × 2 × 2 × 2 × 48

= 2 × 2 × 2 × 2 × 2 × 24

= 2 × 2 × 2 × 2 × 2 × 2 × 12

= 2 × 2 × 2 × 2 × 2 × 2 × 2 × 6

= 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3

= 28 × 3

5. Simplify:

(i) ((25)2 × 73)/ (83 × 7)

Answer: 98

Explanation: To simplify, let's convert the available numbers into exponents.

8 can be written as: 2 × 2 × 2= 23

Substituting the value of 8 in the expression,

((25)2 × 73)/ (((23)3 × 7)

= (210 × 73)/ (29 × 7)

= (210 - 9 × 73 - 1)

=(21 × 72)

= 2 × 49

= 98

(ii) (25 × 52 × t8)/ (103 × t4)

Answer: 5t4/8

Explanation: To simplify, let's convert the available numbers into exponents.

25 can be written as: 5 × 5 = 52

103 can be written as:

23 × 53

Substituting the value of 25 and 103 in the expression,

(52 × 52 × t8)/ (23 × 53 × t4)

= (52 + 2 - 3 × t8 - 4)/23

=(51 × t4)/23

= 5t4/8

(iii) (35 × 105 ×25)/ (57 × 65)

Answer: 1

Explanation: To simplify, let's convert the available numbers into exponents.

25 can be written as: 5 × 5 = 52

105 can be written as:

25 × 55

65 can be written as:

25 × 35

Substituting the value of 25, 105, and 65 in the above expression, we get:

(35 × 25 × 55 × 52)/ (57 × 25 × 35)

= (35 - 5 × 25 - 5 × 55 + 2 - 7)

= (30 × 20 × 50)

= (1 × 1 × 1)

= 1

Exercise 13.3

1. Write the following numbers in the expanded forms:

279404

279404 = 200000 + 70000 + 9000 + 400 + 4

Expanded form:

= 2 × 105 + 7 × 104 + 9 × 103 + 4 × 102 + 0 × 101 + 4 × 100

3006194

3006194 = 3000000 + 6000 + 100 + 90 + 4

Expanded form:

= 3 × 106 + 0 × 105 + 0 × 104 + 6 × 103 + 1 × 102 + 9 × 101 + 4 × 100

2806196

2806196 = 2000000 + 800000 + 6000 + 100 + 90 + 6

Expanded form:

= 2 × 106 + 8 × 105 + 0 × 104 + 6 × 103 + 1 × 102 + 9 × 101 + 6 × 100

120719

120719 = 100000 + 20000 + 700 + 10 + 9

Expanded form:

1 × 105 + 2 × 104 + 0 × 103 + 7 × 102 + 1 × 101 + 9 × 100

20068

20068 = 20000 + 60 + 8

Expanded form:

2 × 104 + 0 × 103 + 0 × 102 + 6 × 101 + 8 × 100

2. Find the number from each of the following expanded forms:

(a) 8 × 104 + 6 × 103 + 0 × 102 + 4 × 101 + 5 × 100

Answer: 86045

Explanation: 80000 + 6000 + 0 + 40 + 5

= 86045

(b) 4 × 105 + 5 × 103 + 3 × 102 + 2 × 100

Answer: 405302

Explanation: 400000 + 5000 + 300 + 2

= 405302

(c) 3 × 104 + 7 × 102 + 5 × 100

Answer: 30705

Explanation: 30000 + 700 + 5

30705

(d) 9 × 105 + 2 × 102 + 3 × 101

Answer: 900230

Explanation: 900000 + 200 + 30

900230

3. Express the following numbers in standard form:

(i) 5,00,00,000

Answer: 5 × 107

Explanation: There are seven zeroes present in the number 5,00,00,000. Hence, it can be represented as:

5 × 107

(ii) 70,00,000

Answer: 7 × 106

Explanation: There are six zeroes present in the number 70,00,000. Hence, it can be represented as:

7 × 106

(iii) 3,18,65,00,000

Answer: 3.1865 × 109

Explanation: There are five zeroes present in the number 3,18,65,00,000. Hence, it can be represented as:

31865 × 105

Let's convert the number into the single decimal number.

3.1865 × 104 × 105

= 3.1865 × 109

(iv) 3,90,878

Answer: 3.90878 × 105

Explanation: 3,90,878 can be represented as:

3.90878 × 105

(v) 39087.8

Answer: 3.90878 × 104

Explanation: 39087.8 can be represented as:

3.90878 × 104

(vi) 3908.78

Answer: 3.90878 × 103

Explanation: 3908.78 can be represented as:

4. Express the number appearing in the following statements in standard form.

(a) The distance between Earth and Moon is 384,000,000 m.

Answer: 3.84 × 108 m

Explanation: 384,000,000 m can be represented as:

384 × 106

= 3.84 × 102 × 106

= 3.84 × 108 m

(b) Speed of light in vacuum is 300,000,000 m/s.

Answer: 3 × 108 m/s

Explanation: 300,000,000 m can be represented as:

3 × 108 m/s

(c) Diameter of the Earth is 1,27,56,000 m.

Answer: 1.2756 × 107 m

Explanation: 1,27,56,000m can be represented as:

1.2756 × 107 m

(d) Diameter of the Sun is 1,400,000,000 m.

Answer: 1.4 × 109 m

Explanation: 1,400,000,000 m can be represented as:

1.4 × 109 m

(e) In a galaxy there are on an average 100,000,000,000 stars.

Answer: 1 × 1011

Explanation: 100,000,000,000 stars can be represented as:

1011

Or

1 × 1011

(f) The universe is estimated to be about 12,000,000,000 years old.

Answer: 1.2 × 1010 years

Explanation: 12,000,000,000 can be represented as:

1.2 × 1010 years

(g) The distance of the Sun from the centre of the Milky Way Galaxy is estimated to be 300,000,000,000,000,000,000 m.

Answer: 3 × 1020 m

Explanation: There are twelve zeroes in the number 300,000,000,000,000,000,000. Hence, it can be represented as:

3 × 1020 m

(h) 60,230,000,000,000,000,000,000 molecules are contained in a drop of water weighing 1.8 gm.

Answer: 6.023 × 1022

Explanation: 60,230,000,000,000,000,000,000 molecules can be represented as:

6.023 × 1022 molecules

(i) The earth has 1,353,000,000 cubic km of sea water.

Answer: 1.353 × 109 km3

Explanation: 1,353,000,000 cubic km can be represented as:

1.353 × 109 cubic km

(j) The population of India was about 1,027,000,000 in March, 2001.

Answer: 1.027 × 109

Explanation: 1,027,000,000 can be represented as:

1.027 × 109






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