# 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)

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

Video Solution
Exponents And Powers
Ex 13.3 | Question 2

## 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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