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

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

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

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

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

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

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

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

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

  
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