NCERT Solutions for Class 7 Maths Exercise 13.3

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NCERT solutions for Maths Exponents and Powers Download as PDF

NCERT Solutions for Class 7 Maths Exercise 13.3

NCERT Solutions for Class 7 Maths Exponents and Powers

Class –VII Mathematics (Ex. 13.3)
Question 1.Write the following numbers in the expanded form:

279404, 3006194, 2806196, 120719, 20068

Answer:

(i) 2,79,404 = 2,00,000 + 70,000 + 9,000 + 400 + 00 + 4

= 2 x 100000 + 7 x 10000 + 9 x 1000 + 4 x 100 + 0 x 10 + 4 x 1

= {tex}2 \times {10^5} + 7 \times {10^4} + 9 \times {10^3} + 4 \times {10^2} + 0 \times {10^1} + 4 \times {10^0}{/tex}

(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 + 1 x 100 + 9 x 10 +

4 x 1

= {tex}3 \times {10^6} + 0 \times {10^5} + 0 \times {10^4} + 6 \times {10^3} + 1 \times {10^2} + 9 \times 10 + 4 \times {10^0}{/tex}

(iii) 28,06,196 = 20,00,000 + 8,00,000 + 0 + 6,000 + 100 + 90 + 6

= 2 x 1000000 + 8 x 100000 + 0 x 10000 + 6 x 1000 + 1 x 100 + 9 x 10 +

6 x 1

= {tex}2 \times {10^6} + 8 \times {10^5} + 0 \times {10^4} + 6 \times {10^3} + 1 \times {10^2} + 9 \times 10 + 6 \times {10^0}{/tex}

(iv) 1,20,719 = 1,00,000 + 20,000 + 0 + 700 + 10 + 9

= 1 x 100000 + 2 x 10000 + 0 x 1000 + 7 x 100 + 1 x 10 + 9 x 1

= {tex}1 \times {10^5} + 2 \times {10^4} + 0 \times {10^3} + 7 \times {10^2} + 1 \times {10^1} + 9 \times {10^0}{/tex}

(v) 20,068 = 20,000 + 00 + 00 + 60 + 8

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

= {tex}2 \times {10^4} + 0 \times {10^3} + 0 \times {10^2} + 6 \times {10^1} + 8 \times {10^0}{/tex}


NCERT Solutions for Class 7 Maths Exercise 13.3

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

(a) {tex}\;8 \times {10^4} + 6 \times {10^3} + 0 \times {10^2} + 4 \times {10^1} + 5 \times {10^0}{/tex}

(b) {tex}4 \times {10^5} + 5 \times {10^3} + 3 \times {10^2} + 2 \times {10^0}{/tex}

(c) {tex}3 \times {10^4} + 7 \times {10^2} + 5 \times {10^0}{/tex}

(d) {tex}9 \times {10^5} + 2 \times {10^2} + 3 \times {10^1}{/tex}

Answer:

(a){tex}\;8 \times {10^4} + 6 \times {10^3} + 0 \times {10^2} + 4 \times {10^1} + 5 \times {10^0}{/tex}

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

= 80000 + 6000 + 0 + 40 + 5

= 86,045

(b) {tex}4 \times {10^5} + 5 \times {10^3} + 3 \times {10^2} + 2 \times {10^0}{/tex}

= 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) {tex}3 \times {10^4} + 7 \times {10^2} + 5 \times {10^0}{/tex}

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

= 30000 + 0 + 700 + 0 + 5

= 30,705

(d) {tex}9 \times {10^5} + 2 \times {10^2} + 3 \times {10^1}{/tex}

= 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


NCERT Solutions for Class 7 Maths Exercise 13.3

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:

(i) 5,00,00,000 = 5 x 1,00,00,000 = {tex}5 \times {10^7}{/tex}

(ii) 70,00,000 = 7 x 10,00,000 = {tex}7 \times {10^6}{/tex}

(iii) 3,18,65,00,000 = 31865 x 100000 = 3.1865 x 10000 x 100000 = {tex}3.1865 \times {10^9}{/tex}

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

(v) 39087.8 = 3.90878 x 10000 = {tex}3.90878 \times {10^4}{/tex}

(vi) 3908.78 = 3.90878 x 1000 = {tex}3.90878 \times {10^3}{/tex}


NCERT Solutions for Class 7 Maths Exercise 13.3

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:

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

= 384 x 1000000 m = 3.84 x 100 x 1000000

= {tex}3.84 \times {10^8}{/tex} m

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

= 3 x 100000000 m/s

= {tex}3 \times {10^8}{/tex} m/s

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

= 12756 x 1000 m = 1.2756 x 10000 x 1000 m

= {tex}1.2756 \times {10^7}{/tex} 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

= {tex}1.4 \times {10^9}{/tex} m

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

= 1 x 100,000,000,000

= {tex}1 \times {10^{11}}{/tex}

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

= 12 x 1000,000,000 years

= 1.2 x 10 x 1000,000,000 years

= {tex}1.2 \times {10^{10}}{/tex} years

(g) Distance of the Sun from the = 300,000,000,000,000,000,000 m

centre of the Milky Way Galaxy = 3 x 100,000,000,000,000,000,000 m

= {tex}3 \times {10^{20}}{/tex} m

(h) Number of molecules in a drop = 60,230,000,000,000,000,000,000

of water weighing 1.8 gm = 6023 x 10,000,000,000,000,000,000

= 6.023 x 1000 x 10,000,000,000,000,000,000

= {tex}6.023 \times {10^{22}}{/tex}

(i) The Earth has Sea water = 1,353,000,000 {tex}k{m^3}{/tex}

= 1,353 x 1000000 {tex}k{m^3}{/tex}

= 1.353 x 1000 x 1000,000 {tex}k{m^3}{/tex}

= {tex}1.353 \times {10^9}{/tex} {tex}k{m^3}{/tex}

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

= 1027 x 1000000

= 1.027 x 1000 x 1000000

= {tex}1.027 \times {10^9}{/tex}

NCERT Solutions for Class 7 Maths Exercise 13.3

NCERT Solutions for Class 7 Maths Exercise 13.3 PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 7 Maths includes text book solutions from Class 7 Maths Book . NCERT Solutions for CBSE Class 7 Maths have total 15 chapters. 7 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 7 solutions PDF and Maths ncert class 7 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide.

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