CLASS-7 SUBJECT MATHS CHAPTER-13 EXERCISE 13.3 (EXPONENTS AND POWERS)

 EVENTS CONVENT HIGH SCHOOL

31/01/2022      CLASS- 7   SESSION 2021-22
SUBJECT : MATHS

CHAPTER-13 (EXERCISE-13.3)
exponents and powers

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Question 1.Write the following numbers in the e×panded forms:

279404, 3006194, 2806196, 120719, 20068
Solution:
(i) 279404 = 2 × 100000 + 7 × 10000 + 9 × 1000 + 4 × 100 + 0 × 10 + 4
= 2 × 105 + 7 × 104 + 9 × 1032 + 4 × 102 + 0 × 101 + 4 × 100
(ii) 3006194 = 3 × 1000000 + 0 × 100000 + 0 × 10000 + 6 × 1000 + 1 × 100 + 9 × 10 + 4
= 3 × 106 + 0 × 105 + 0 × 104 + 6 × 103 + 1 × 102 + 9 × 101 + 4 × 100
(iii) 2806196 = 2 × 1000000 + 8 × 100000 + 0 × 10000 + 6 × 1000 + 1 × 100 + 9 × 10 + 6
= 2 × 106 + 8 × 105 + 0 × 104 + 6 × 103 + 1 × 102 + 9 × 101 + 6 × 100
(iv) 120719 = 1 × 100000 + 2 × 10000 + 0 × 1000 + 7 × 100 + 1 × 10 + 9
= 1 × 105 + 2 × 104 + 0 × 103 + 7 × 102 + 1 × 101 + 9 × 100
(v) 20068 = 2 × 10000 + 0 × 1000 + 0 × 100 + 6 × 10 + 8
= 2 × 104 + 0 × 103 + 0 × 102 + 6 × 101 + 8 × 100 

 Question 2.Find the number from each of the following expanded forms:
(a) 8 × 104 + 6 × 103 + 0 × 102 + 4 × 101 + 5 × 100
(b) 4 × 105 + 5 × 103 + 3 × 102 + 2 × 100
(c) 3 × 104 + 7 × 102 + 5 × 100
(d) 9 × 105 + 2 × 102 + 3 × 101
Solution:
(a) 8 × 104 + 6 × 103 + 0 × 102 + 4 × 101 + 5 × 100
= 8 × 10000 + 6 × 1000 + 0 × 100 + 4 × 10 + 5 × 1
= 80000 + 6000 + 0 + 40 + 5 = 86045

(b) 4 × 105 + 5 × 103 + 3 × 102 + 2 × 100
= 4 × 100000 + 5 × 1000 + 3 × 100 + 2 × 1
= 400000 + 5000 + 300 + 2 = 405302

(c) 3 × 104 + 7 × 102 + 5 × 100
= 3 × 10000 + 7 × 100 + 5 × 1
= 30000 + 700 + 5 = 30705

(d) 9 × 105 + 2 × 102 + 3 × 101
= 9 × 100000 + 2 × 100 + 3 × 10
= 900000 + 200 + 30 = 900230

Question 3.Express the following numbers in standard form:
(i) 5,00,00,000
(ii) 70,00,000
(iii) 3,18,65,00,000
(iv) 3,90,878
(v) 39087.8
(vi) 3908.78
Solution:
(i) 5,00,00,000 = 5 × 1077
(ii) 70,00,000 = 7 × 106
(iii) 3,18,65,00,000 = 3.1865 × 109
(iv) 3,90,878 = 3.90878 × 105
(v) 39087.8 = 3.90878 × 104
(vi) 3908.7 8 = 3.90878 × 103

CLASS-7 SUBJECT MATHS CHAPTER-13 EXERCISE (13.2) EXOPONENTS AND POWERS

 EVENTS CONVENT HIGH SCHOOL

27/01/2022      CLASS- 7   SESSION 2021-22
SUBJECT : MATHS

CHAPTER-13 (EXERCISE13.2)
EXPONENTS AND POWERS

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 Question 1.Using laws of e×ponents, simplify and write the answer in e×ponential form:

(i) 32 × 34 × 38
(ii) 615 ÷ 610
(iii) a3 × a2
(iv) 7x × 72
(v) (52)3 ÷ 53
(vi) 25 × 55

Solution:
(i) 32 × 34 × 38 = 32+4+8 = 314 [am ÷ an = am+n]
(ii) 615 ÷ 610 = 615-10 = 65 [am ÷ an = am-n]
(iii) a3 × a2 = a3+2 = a5 [am × an = am+n]
(iv) 7x × 72 = 7x+2 [am × an = am+n]
(v) (52)3 ÷ 53 = 52×3 ÷ 53 = 56 ÷ 53 = 56-3 = 53 [(a3)n = amn, am ÷ an = am-n]
(vi) 25 × 55 = (2 × 5)5 = 105 [am × bm = (ab)m]

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

Solution: