CBSE students can refer to NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Ex 13.3 Textbook Questions and Answers are provided by experts in order to help students secure good marks in exams.

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

Question 1.

Write the following numbers in the expanded forms :

Solution:

(i) 279404 = 2 × 100000 + 7 × 10000 x 9 × 1000 + 4 × 100 + 0 × 10 + 4 × 1

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

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

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

+ 1 × 10^{2} + 9 × 10^{1} + 4 × 10°

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

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

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

= 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 × 1

= 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}

Solution:

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

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

= 86045

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

Solution:

4 × 10^{5} + 5 × 10^{3} + 3 × 10^{2} + 2 × 10^{0}

= 4 × 100000 + 5 × 1000 + 3 × 100 + 2

= 405302

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

Solution:

3 × 10^{4} + 7 × 10^{2} + 5 × 1

= 3 × 10000 + 7 × 100 + 5 × 1

= 30705

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

Solution:

9 × 10^{5} + 2 × 10^{2} + 3 × 10^{1}

= 9 × 100000 + 2 × 100 + 30

= 900230

Question 3.

Express the following numbers in standard form:

(i) 5,00,00,000

Solution:

5,00,00,000 = 5 × 10000000 = 5 × 10^{7}

(ii) 70,00,000

Solution:

70,00,000 = 7 × 1000000 = 7 × 10^{6}

(iii) 3,18,65,00,000

Solution:

3,18,65,00,000 = 3.1865 × 1000000000 = 3.1865 × 10^{9}

(iv) 3,90,878

Solution:

3,90,878 = 3.90878 × 100000 = 3.90878 × 10^{5}

(v) 39087.8

Solution:

39087.8 = 3.90878 × 10000 = 3.90878 × 10^{4}

(vi) 3908.78

Solution:

3908.78 = 3.90878 × 1000 = 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 384,000,000 m.

Solution:

The mean distance between Earth and Moon = 384,000,000 m = 3.84 × 100000000 m = 3.84 × 10^{8} m

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

Solution:

Speed of light in vaccum

= 300,000,000 m/s

= 3.0 × 100000000 m/s

= 3.0 × 10^{8} m/s

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

Solution:

Diameter of the Earth 1,27,56,000 m

= 1.2756 × 10000000 m = 1.2756 × 10^{7}

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

Solution:

Diameter of the Sun

= 1,400,000,000 m = 1.4 × 1000000000 m = 1.4 × 10^{9} m

(e) In a galaxy there are on4m average 100,000,000,000 stars.

Solution:

In a galaxy there are on an average

= 100,000,000,000 stars = 1 × 100000000000 stars = 1 × 10^{11 }stars

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

Solution:

The universe is estimated to be 12,000,000,000 years old

= 12 × 1,000,000,000 = 1.2 × 10^{10} year

(g) The distance of the Sun from the center of the Milky Way Galaxy is estimated to be 300,000,000,000,000,000,000 m.

Solution:

The distance of Sun from the centre of the Milky Way Galaxy is estimated to be

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

= 3 × 100000000000000000000

= 3 × 10^{20} m

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

Solution:

Number of molecules contained in a drop of water weighing 1.8 gm = 60,230,000,000,000,000,000,000

= 6.023 × 10000000000000000000000 = 6.023 × 10^{20}

(i) The Earth has 1,353,000,000 cubic km of seawater.

Solution:

The Earth has 1,353,000,000 cubic km of seawater i.e.,

1.353 × 1,000,000,000 = 1.353 × 10^{9} cubic km.

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

Solution:

The population of India was about in March 2001 = 1,027,000,000 = 1.027 × 1000000000 = 1.027 × 10^{9}