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I need to play with a lot of powers such as 10^-3. 1E-3 does not work for it. Is there any short form for it?

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I'm surprised there isn't a question about this (i.e. entering numbers in scientific notation) already.

To enter $3\times10^{-3}$, you can write 3*^-3.

For further reference, see Input Syntax: Numbers.

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    $\begingroup$ Yeah... it's indeed very surprising. Even Google does a bad job of leading to the correct syntax (of course that's before this answer became popular — now this is one of the top answers). $\endgroup$ – Shashank Sawant Oct 31 '14 at 8:44
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    $\begingroup$ That notation looks SO funny and wrong to me. Where did it come from, and why not use the old E notation which many people already know? $\endgroup$ – Ralph Dratman May 2 '17 at 18:07
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    $\begingroup$ @Ralph: Because in Mathematica E already means $e\approx 2.718$, so 3E-3 is interpreted as $3e-3$. $\endgroup$ – Rahul May 2 '17 at 18:38
  • $\begingroup$ It's so easy to think of and to write 3*10^-3 that people might not be motivated to look for another way. I've seen hundreds of notebooks and only very rarely seen the *^ notation. $\endgroup$ – Reb.Cabin Oct 13 '18 at 3:17
  • $\begingroup$ The E notation works when importing data from a file with a CSV extension and in which the data values are separated by commas. $\endgroup$ – CElliott Aug 21 at 14:32
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I ran into this as well teaching some solubility chemistry (it's logs all the way down). The notation can get in the way, but most students can keep up with 1×10^-5 syntax - just don't forget to wrap it in brackets i.e.:

1*^-10/1*^-5 == (1×10^-10)/(1×10^-5)
(* True *)

NB: the × in 1×10 is added automatically when pushing space.

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