# 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) $$4\times {{10}^{14}};3\times {{10}^{17}}$$

## 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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