Ex 13.1 Q8 Exponents and Powers Solution- NCERT Maths Class 7

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Question

Compare the following numbers:

(i) \(2.7\times {{10}^{12}} ; \,k1.5\times {{10}^{8}}\)

(ii) \(4\times {{10}^{14}};3\times {{10}^{17}}\) 

 Video Solution
Exponents And Powers
Ex 13.1 | Question 8

Text Solution

What is known? 

Two numbers with base \(10\) but different powers.

What is unknown? 

Out of the given two numbers, which number is greater or smaller.

Reasoning:

In this question, simplify the numbers and decide which one is greater. Another way is to look at the power of \(10\). The number with higher power of \(10\) is greater than the other.

Steps:

(i) In numbers,\(2.7 \! \times \! 10^{12} \) and \(1.5 \! \times \! 10^8\)

\[\begin{align}2.7 \times 10^{12} &= 2.7 \times 12\,\rm{ times}\,\\10 &= 2.7 \times 1000000000000 \\&= 27,00,00,00,00,000\end{align}\]

And

\[\begin{align}1.5 \times 10^8 &= 1.5 \times 8\, \rm{times}\\10 &= 1.5 \times 100000000\\&= 15,00,00,000\end{align}\]

So, \(2.7 \! \times \! 10^{12} \) is greater than \(1.5 \! \times \! 10^8\)

(ii) In numbers, \(4 \! \times \! 10^{14}; \;3 \! \times \! 10^{17}\) 

\[\begin{align}4 \times 10^{14}&= 4 \times 14\,\rm{times} \\10&= 4 \times 100000000000000 \\&= 4,00,00,00,00,00,000\end{align}\]

And

\[\begin{align}3 \! \times \! 10^{17} &\!=\!3\!\times\!17\,\rm{ times }\\10 &\!=\! 3\! \times\! 100000000000000000 \\&\!=\! 3,00,00,00,00,00,00,00,000\end{align}\]

So, \(3 \! \times \! 10^{17} \) is greater than \(4 \! \times \! 10^{14}\)

  
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