EX.13.3 Q1 Exponents-and-Powers Solutions- NCERT Maths class 7

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Question

Write the following numbers in the expanded forms:

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

Text 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) \(20068\)

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

  
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