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I'm doing a Mock Exam and I'm not sure how to do this question. I know how to multiply however I'm not sure how to do $10$ and then the $-3$ inverse. I think it is cubed ($-1000$) however I'm not sure if it is right. This is a non-calculator paper by the way. Thank you.

José Carlos Santos
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1 Answers1

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For integers $k\neq 0$

$$a\times b^{-k} = \dfrac a{b^k}$$

So, in your case,

$$4.5 \times 10^{-3} = \frac {4.5}{10^3} = \frac {4.5}{1000} = 0.0045$$

amWhy
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  • why would you devide $4$ by $1000$. I understand what you are writing however I'm not sure why you devide. –  Oct 24 '13 at 17:49
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    Because the multiplicative inverse of $10^{-3}=\dfrac 1{10^3}$ is $10^3$. So multiplying by $10^{-3}$ is equivalent to dividing by $10^3$. – amWhy Oct 24 '13 at 17:50
  • No, $10^{-3}$ $\textbf{is}$ $\frac{1}{10^3}$; its multiplicative inverse is $10^3$. – Eric Tressler Oct 24 '13 at 17:52
  • Is the answer $0.0045$? –  Oct 24 '13 at 17:53
  • Yes, the answer is 0.0045. amWhy seems to have misread your question. – Eric Tressler Oct 24 '13 at 19:30
  • @Eric and Honky: yes, You're both correct. Indeed, I misread the question and was working with $4 \times ...$ instead of $4.5\times ...$ Sorry for any inadvertent confusion. Now edited and updated. – amWhy Oct 24 '13 at 19:33