# 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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