EX.13.3 Q2 Exponents-and-Powers Solutions- NCERT Maths class 7

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Question

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)

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

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

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

  
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