The document NCERT Solutions(Part - 2) - Exponents and Powers Class 7 Notes | EduRev is a part of the Class 7 Course Mathematics (Maths) Class 7.

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**Exercise 13.3 **

**Question 1: **

**Write the following numbers in the expanded form: **

**279404, **

**3006194, **

**2806196, **

**120719, **

**20068 **

**Answer 1: **

**(i) 2,79,404 **

= 2,00,000 + 70,000 + 9,000 + 400 + 00 + 4

= 2x100000 + 7x 10000+ 9x1000 + 4 x 100+ 0x 10 + 4x1

= 2x10^{5}+7x10^{4} +9x10^{3} + 4 x10^{2}+ 0x10^{1}+4x10^{0}

**(ii) 30,06,194 **

= 30,00,000 + 0 + 0 + 6,000 + 100 + 90 + 4

= 3 x 1000000 + 0 x 100000 + 0 x 10000 + 6 x 1000 + 1x100 + 9x10 + 4x1

= 3x10^{6} + 0x10^{5} +0x10^{4} +6 x10^{3}+1x10^{2} +9x10+4x10^{0}

**(iii) 28,06,196 **

= 20,00,000 + 8,00,000 + 0 + 6,000 + 100 + 90 + 6

= 2x1000000 + 8x 100000+ 0x 10000 +6 x 1000 + 1 x 100 + 9 x 10 + 6 x 1

= 2 x10^{6}+8x10^{5}+0x10^{4} + 6x10^{3}+1x10^{2}+9x10+6x10^{0}

**(iv) 1,20,719 **

= 1,00,000 + 20,000 + 0 + 700 + 10 + 9

= 1 x 100000 + 2 x 10000 + 0x 1000 + 7x100 + 1x 10+9x1

= 1 x 10^{5} + 2 x 10^{4 }+ 0 x 10^{3} + 7 x 10^{2} + 1 x 10^{1} + 9 x 10^{0}

**(v)** **20,068 **

= 20,000 + 00 + 00 + 60 + 8

= 2 x 10000 + 0 x 1000 + 0 x 100 + 6 x 10 + 8 x 1

**Question 2: **

**Find the number from each of the following expanded forms: **

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

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

**(c) 3 x 104 + 7 x 102 + 5 x 100 (d) 9 x 105 + 2 x 102 + 3 x 101 **

**Answer 2: **

**(a) **8 x 104 + 6 x 10^{3} + 0 x 10^{2} + 4 x 10^{1} + 5 x 10^{0}

= 8 x 10000 + 6x 1000 + 0 x 100 + 4 x 10 + 5 x 1

= 80000 + 6000 + 0 + 40+5

= 86,045

**(b) **4 x 10^{5} + 5 x 10^{3} + 3 x 10^{2} + 2 x 10^{0}

= 4 x 100000 + 0 x 10000 + 5 x 1000 + 3 x 100 + 0 x 10 + 2 x 1

= 400000 + 0 + 5000 + 3000 + 0 + 2

= 4,05,302

**(c) **3 x 10^{4} + 7 x 10z + 5 x 10^{0}

= 3 x 10000 + 0 x 1000 + 7 x 100 + 0 x 10 + 5 x 1

= 30000 + 0 + 700 + 0 + 5

= 30,705

**(d) **9x 10^{5} + 2 x 10^{2} + 3 x 10^{1}

= 9 x 100000 + 0 x 10000 + 0 x 1000 + 2 x 100 + 3 x 10 + 0 x 1

= 900000 + 0 + 0 + 200 + 30 + 0

= 9,00,230

**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 **

**Answer 3: **

(i) 5,00,00,000 = 5 x 1,00,00,000 = 5 x 10^{7}

(ii) 70,00,000 = 7 x 10,00,000 = 7 x 10^{6}

(iii) 3,18,65,00,000 = 31865 x 100000

= 3.1865 x 10000 x 100000 = 3.1865 x 10^{9}

(iv) 3,90,878 = 3.90878 x 100000 = 3.90878 x 10^{5}

(v) 39087.8 = 3.90878 x 10000 = 3.90878 x 10^{4}

(vi) 3908.78 = 3.90878 x 1000 = 3.90878 x 10^{3}

**Question 4: **

**Express the number appearing in the following statements in standard form: **

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

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

**(c) Diameter of Earth id 1,27,56,000 m. **

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

**(e) In a galaxy there are on an average 100,000,000,0000 stars. **

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

**(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. **

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

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

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

**Answer 4: **

**(a) **The distance between Earth and Moon = 384,000,000 m

= 384x 1000000 m

= 3.84 x 100 x 1000000

= 3.84x10^{8} m

**(b) **Speed of light in vacuum = 300,000,000 m/s

= 3 x 100000000 m/s

= 3x10^{8} m/s

**(c) **Diameter of the Earth = 1,27,50,000 m

= 12756 x 1000 m

= 1.2756 x 10000 x 1000 m

= 1 2756x10^{7} m

**(d) **Diameter of the Sun = 1,400,000,000 m

= 14 x 100,000,000 m

= 1.4 x 10 x 100,000,000 m

= 1.4 x 10^{9} m

**(e) **Average of Stars = 100, 000, 000,000

= 1 x 100,000,000,000

= 1x10^{11}

**(f)** Years of Universe = 12,000,000,000 years

= 12 x 1000,000,000 years

= 1.2 x 10 x 1000,000,000 years

= 1.2 x 10^{10} years

**(g) **Distance of tlie Sun from the centre of the Milky Way Galaxy

= 300,000,000,000,000,000,000 m

= 3 x 100,000,000,000,000,000,000 m

= 3 x 10^{20} m

**(h)** Number of molecules in a drop of water weighing 1.8 gm

= 60,230,000,000,000,000,000,000

= 6023 x 10,000,000,000,000,000,000

= 6,023 x 1000 x 10,000,000,000,000,000,000

= 6.023 x10^{22}

**(i) **The Earth has Sea water = 1,353,000,000 km^{3}

= 1,353 x 1000000 km^{3}

= 1,353 x 1000 x 1000,000 km^{3}

= 1.353x10^{9} km^{3}

**(j)** The population of India = 1,027,000,000

= 1027x1000000 = 1,027x1000x1000000

= 1.027x10^{9}

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