## NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Ex 13.3

- Class 7 Maths Exponents and Powers Exercise 13.1
- Class 7 Maths Exponents and Powers Exercise 13.2
- Class 7 Maths Exponents and Powers Exercise 13.3

**NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Exercise 13.3**

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 × 10^{5} + 7 × 10^{4} + 9 × 10^{32} + 4 × 10^{2} + 0 × 10^{1} + 4 × 10^{0}

(ii) 3006194 = 3 × 1000000 + 0 × 100000 + 0 × 10000 + 6 × 1000 + 1 × 100 + 9 × 10 + 4

= 3 × 10^{6} + 0 × 10^{5} + 0 × 10^{4} + 6 × 10^{3} + 1 × 10^{2} + 9 × 10^{1} + 4 × 10^{0}

(iii) 2806196 = 2 × 1000000 + 8 × 100000 + 0 × 10000 + 6 × 1000 + 1 × 100 + 9 × 10 + 6

= 2 × 10^{6} + 8 × 10^{5} + 0 × 10^{4} + 6 × 10^{3} + 1 × 10^{2} + 9 × 10^{1} + 6 × 10^{0}

(iv) 120719 = 1 × 100000 + 2 × 10000 + 0 × 1000 + 7 × 100 + 1 × 10 + 9

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

(v) 20068 = 2 × 10000 + 0 × 1000 + 0 × 100 + 6 × 10 + 8

= 2 × 10^{4} + 0 × 10^{3} + 0 × 10^{2} + 6 × 10^{1} + 8 × 10^{0}

Question 2.

Find the number from each of the following expanded forms:

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

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

(c) 3 × 10^{4} + 7 × 10^{2} + 5 × 10^{0}

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

Solution:

(a) 8 × 10^{4} + 6 × 10^{3} + 0 × 10^{2} + 4 × 101 + 5 × 10^{0}

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

= 80000 + 6000 + 0 + 40 + 5 = 86045

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

= 4 × 100000 + 5 × 1000 + 3 × 100 + 2 × 1

= 400000 + 5000 + 300 + 2 = 405302

(c) 3 × 10^{4} + 7 × 10^{2} + 5 × 10^{0}

= 3 × 10000 + 7 × 100 + 5 × 1

= 30000 + 700 + 5 = 30705

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

= 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 × 107^{7}

(ii) 70,00,000 = 7 × 10^{6}

(iii) 3,18,65,00,000 = 3.1865 × 10^{9}

(iv) 3,90,878 = 3.90878 × 10^{5}

(v) 39087.8 = 3.90878 × 10^{4}

(vi) 3908.7 8 = 3.90878 × 10^{3}

Question 4.

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

(a) The distance between Earth and Moon is 384.0. 000 m.

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

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

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

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

Solution:

(a) 384,000,000 m = 3.84 × 10^{8} m

(b) 300,000,000 m/s = 3 × 10^{8} m/s

(c) 1,27,56,000 m = 1.2756 × 10^{72} m

(d) 1,400,000,000 m = 1.4 × 10^{9} m

(e) 100,000,000,000 stars = 1 × 10^{11} stars

(f) 12,000,000,000 years old = 1.2 × 10^{10} years old

(g) 300,000,000,000,000,000,000 m = 3 × 10^{20} m

(h) 60, 230, 000, 000, 000, 000, 000, 000 molecules = 6.023 × 10^{22} molecules

(i) 1,353,000,000 cubic km = 1.353 × 10^{9} cubic km

(j) 1,0,27,000,000 = 1.027 × 10^{9}

Aryan says

November 16, 2018 at 8:41 pmThis soluation is correct.

Aryan says

November 16, 2018 at 8:41 pmThis soluation is correct.ggggggg

Numa Sheikh says

February 14, 2019 at 2:44 am“Solution” not soluation