RS Aggarwal 2019,2020 solution class 7 chapter 5 Exponents Exercise 5B

Exercise 5B

Page-92

Question 1:

Express each of the following numbers in standard form:

(i) 538
(ii) 6428000
(iii) 82934000000
(iv) 940000000000
(v) 23000000

Answer 1:

(i) 538 = 5.38 × 102                                        [since the decimal point is moved 2 places to the left]

(ii) 6428000 = 6.428 × 106                             [since the decimal point is moved 6 places to the left]

(iii) 82934000000 = 8.2934 × 1010                [since the decimal point is moved 10 places to the left]

(iv) 940000000000 = 9.4 × 1011                    [since the decimal point is moved 11 places to the left]

(v) 23000000 = 2.3 × 107                               [since the decimal point is moved 7 places to the left]

Question 2:

Express each of the following numbers in standard form:

(i) Diameter of Earth = 12756000 m.
(ii) Distance between Earth and Moon = 384000000 m.
(iii) Population of India in March 2001 = 1027000000.
(iv) Number of stars in a galaxy = 100000000000.
(v) The present age of universe = 12000000000 years

Answer 2:

(i) Diameter of the Earth = 1.2756 × 107 m
     [since the decimal point is moved 7 places to the left]

(ii) Distance between the Earth and the Moon = 3.84 × 108 m
      [since the decimal point is moved 8 places to the left]

(iii) Population of India in March 2001 = 1.027 × 109
       [since the decimal point is moved 9 places to the left]

(iv) Number of stars in a galaxy = 1.0 × 1011
       [since the decimal point is moved 11 places to the left]

(v) Present age of the universe = 1.2 × 1010 years
      [since the decimal point is moved 10 places to the left]

Page-93

Question 3:

Write the following numbers in expanded form:

(i) 684502
(ii) 4007185
(iii) 5807294
(iv) 50074

Answer 3:

(i) 684502 = 6 x 105 + 8 x 104 + 4 x 103 + 5 x 102 + 0 x 101 + 2 x 100
(ii) 4007185 = 4 x 106 + 0 x 105 + 0 x 104 + 7 x 103 + 1 x 102 + 8 x 101 + 5 x 100
(iii) 5807294 = 5 x 106 + 8 x 105 + 0 x 104 + 7 x 103 + 2 x 102 + 9 x 101 + 4 x 100
(iv) 50074 = 5 x 104 + 0 x 103 + 0 x 102 + 7 x 101 + 4 x 100

Note: a0 = 1

Question 4:

Write the numeral whose expanded form is given below:

(i) 6 × 104 + 3 × 103 + 0 × 102 + 7 × 101 + 8 × 100
(ii) 9 × 106 + 7 × 105 + 0 × 104 + 3 × 103 + 4 × 102 + 6 × 101 + 2 × 100
(iii) 8 × 105 + 6 × 104 + 4 × 103 + 2 × 102 + 9 × 101 + 6 × 100

Answer 4:

(i) 6 × 104 + 3 × 103 + 0 × 102 + 7 × 101 + 8 × 100
      = 6 x 10000 + 3 x 1000 + 0 x 100 + 7 x 10 + 8 x 1 = 63078
     
(ii) 9 × 106 + 7 × 105 + 0 × 104 + 3 × 103 + 4 × 102 + 6 × 101 + 2 × 100
      = 9 x 1000000 + 7 x 100000 + 0 x 10000 + 3 x 1000 + 4 x 100 + 6 x 10 + 2 x 1 = 9703462

(iii) 8 × 105 + 6 × 104 + 4 × 103 + 2 × 102 + 9 × 101 + 6 × 100
       = 8 x 100000 + 6 x 10000 + 4 x 1000 + 2 x 100 + 9 x 10 + 6 x 1 = 864296

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