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How many numbers are written in scientific notation?

  • $\sqrt7\times10^{-20}$
  • $5.3\times2^{10}$
  • $(\frac13)^{-1}\times10^{15}$

$1)\text{zero}\qquad\qquad2)1\qquad\qquad3)2\qquad\qquad4)3$

We know that in base $10$ the scientific notation of a number is in the form $c\times10^n$ where $c$ is a number between $1$ and $10$ (not including $10$) and $n\in\mathbb{Z}$. Hence the second number ($5.3\times2^{10}$) is excluded. the third number is the same as $3\times10^{15}$ and I think it is written in scientific notation but for the first one I have doubts because although $\sqrt7\in[1,10)$ but haven't' seen this form of number as a scientific notation before.

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Etemon
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    That depends entirely on how you have the notion of "scientific notation" defined, and there is some leeway with how that is done. It is common to require the number $c$ to be written in decimal format with no repeated trailing nines as well as to require $1\leq |c|<10$ so as to have only one valid representation for each number possible in which case I would say none of them are in (normalized) scientific notation... but I could see an argument that the other two should be considered to be as well. – JMoravitz May 25 '21 at 18:53
  • @JMoravitz Thanks for the help. I agree, It seems the question isn't posed very well. – Etemon May 25 '21 at 19:10

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