Exercise 13.3 Exponents-and-Powers -NCERT Solutions Class 7

Go back to  'Exponents and Powers'

Chapter 13 Ex.13.3 Question 1

Write the following numbers in the expanded forms:

 \(279404,3006194,2806196,\\\qquad120719,20068\)

Solution

Video Solution

Reasoning:

Expanded form of number means expressing a number using powers of \(10\) as exponents.

(i) \(279404\)

\(\begin{align}&=\!\left[\begin{array} =2 \times 100000 + 7 \times 10000 +\\ 9 \times  1000 + 4 \times 100 +\\ 0 \times 10 + 4 \times 1\end{array} \right]\\&=\!\left[\begin{array}=2 \times {{10}^5} + 7 \times {{10}^4} + \\9 \times {{10}^3} + 4 \times {{10}^2} +\\ 0 \times {{10}^1} + 4 \times {{10}^0}\end{array} \right]\end{align}\)

(ii) \(3006194\)

\(\begin{align} &=\! \left[\begin{array} =  3  \times 1000000 + \\   0   \times 10000 + 0   \times 10000 \\  + 6 \times 1000 + 1   \times 100 \\ + 9 \times 10 + 4 \times 1\end{array} \right]\\&=  \left[\begin{array}=   3   \times   {{10}^6}+0\times{{10}^5}   +\\  0\times   {{10}^4}   +   6\times {{10}^3}   +\\1   \times{{10}^2}   +   9   \times   {{10}^1}   +\\   4   \times   {{10}^0}\end{array} \right]\end{align}\)

(iii)  \(2806196\)

\(\begin{align}&=\left[\begin{array} = 2 \times 10000 + 0 \times 1000 + \\ 0 \times 100 + 6 \times10 + \\ 8 \times 1\end{array} \right]\\&=\left[\begin{array}= 2 \times {{10}^4} + 0 \times {{10}^3} +\\ 0 \times {{10}^2} + 6 \times {{10}^1} + \\ 8 \times {{10}^0}\end{array} \right]\end{align}\)

(iv)  \(120719\)

\(\begin{align}&=\! \left[\begin{array} = 1 \times 100000 + 2 \times 10000 + \\ 0 \times 1000 + 7 \times 100 + \\ 1 \times 10 + 9 \times 1\end{array} \right]\\&=\! \left[\begin{array} = 1 \times {10}^5 + 2 \times {10}^4 + \\ 0 \times {10}^3 + 7 \times {10}^2 + \\ 1 \times {10}^1 + 9 \times {10}^0\end{array} \right]\end{align}\)

(v) \(20068\)

\(\begin{align}&=\left[\begin{array}  = 2 \times 10000 + 0 \times 1000 +\\ 0 \times 100 + 6 \times 10 + 8 \times 1\end{array} \right]\\&=\left[\begin{array}=2 \times {{10}^4} + 0 \times {{10}^3} + 0 \times\\ {{10}^2} + 6 \times {{10}^1} + 8 \times {{10}^0}\end{array}\right]\end{align}\)

Chapter 13 Ex.13.3 Question 2

Find the number from each of the following expanded forms:

(a)

\(\left[ \begin{align} & 8\times {{10}^{4}}+6\times {{10}^{3}}+0\times \\ & {{10}^{2}}+4\times {{10}^{1}}+5\times {{10}^{0}} \\ \end{align} \right]\)

(b)

\(4  \! \times \!  10^5 \! + \! 5  \! \times \!  10^3  \! + \!  3  \!  \times \!  10^2  \! + \!  2  \! \times \!  10^0\)

(c)

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

(d)

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

Solution

Video Solution

Reasoning:

Expressing a number means we have to expand the following powers of \(10.\)

(a) 

\(\left[ \begin{align} & 8\times {{10}^{4}}+6\times {{10}^{3}}+0\times \\ & {{10}^{2}}+4\times {{10}^{1}}+5\times {{10}^{0}} \\ \end{align} \right]\)

\[\begin{align} & =\left[ \begin{array} & 8\times 10000+6\times 1000+ \\ 0\times 100+4\times 10+5\times 1 \\ \end{array} \right] \\ & =80000+6000+0+40+5 \\ & =86045 \\ \end{align}\]

 (b) 

\(4 \! \times \! {{10}^5} \! + \! 5 \! \times \! {{10}^3} \! + \! 3 \! \times \! {{10}^2} \! + \! 2 \times \! {{10}^0}\)

\[\begin{align} & =\!\left[ \begin{array} & 4\times 100000+ 0\times 10000+\\ 5\times 1000+3\times 100+ \\0\times 10+2\times 1  \end{array}\right] \\ & =\!\left[ \begin{array} &400000+0+5000\\+300+0+2 \end{array}\right]\\ & = 405302   \end{align}\]

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

\[\begin{align}  & =\left[ \begin{array}  & 3\times 10000+0\times 10000+ \\  7\times 100+0\times 10+5\times 1 \\ \end{array} \right] \\  & =30000+0+700+0+5 \\  & =30705 \\ \end{align}\]

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

\[\begin{align} & =\left[ \begin{array}& 9\times 10000+0\times 10000+ \\ 0\times 1000+ 2\times 100+ \\ 3\times 10+0\times 1  \end{array} \right] \\ & =900000+0+0+200+30+0 \\ & =900230 \\ \end{align}\]

Chapter 13 Ex.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) \(3908.78\)

Solution

Video Solution

Reasoning:

Standard form of numbers is used in case of large numbers. Large numbers can be expressed using exponents of \(10\).

(i)

\(5,00,00,000= 5\times{{10}^7}\)

(ii)

\(70,00,000 = 7 \times {{10}^6}\)

(iii)

\(3,18,65,00,000= 3.1865 \times {{10}^9}\)

(iv)

\(3,90,878= 3.90878 \times {{10}^5}\)

(v)

\(39087.8= 3.90878 \times {{10}^4}\)

(vi)

\(3908.78= 3.90878 \times {{10}^3}\)

Chapter 13 Ex.13.3 Question 4

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

(a) The distance between Earth and Moon is \(384,000,000 \rm\, m\)

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

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

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

(e) In a galaxy there are on 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 \(300,000,000,000,000,000,000 \rm\,m\)

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

(i) The earth has \(1,353,000,000\) cubic \(\rm{km}\) of sea water

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

Solution

Video Solution

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

Standard Form \(= 3.84\times10^{8} \rm\, m\)

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

Standard Form \(= 3\times10^{8} \rm \, m/s\)

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

Standard Form \(= 1.2756\times10^{7}\rm\, m\)

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

Standard Form \(= 1.4\times10^{9} \rm\,m\)

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

Standard Form \(= 1\times10^{11}\) stars

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

Standard Form \(= 1.2\times10^{10} \)years old

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

Standard Form \(= 3\times10^{20}\rm\, m\)

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

Standard Form \(= 6.023\times10^{22}\) molecules

(i) The earth has \(1,353,000,000\) cubic \(\rm{km}\) of sea water.

Standard Form \(= 1.353\times10^{9} \rm cubic \,\rm\, km\)

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

Standard Form \(= 1.027\times10^{9}\)

  
Download Cuemath NCERT App
Related Sections
Related Sections
Instant doubt clearing with Cuemath Advanced Math Program
0