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My daughter is learning scientific notation in school, and her textbook says something to the effect of this:

Scientific notation is a method of writing numbers as the product of two factors where the first factor is a number greater than or equal to 1 but less than 10 and the second factor is a power of 10.

The teacher is taking this to mean that you cannot express a negative number in scientific notation. So that e.g.

$-4 * 10^{50}$

would not be valid scientific notation because -4 is less than 1.

Is there such a view of scientific notation? It certainly doesn't jive with my memory (or wikipedia), or is that description just deficient, and should better read:

Scientific notation is a method of writing numbers as the product of two factors where the first factor is a number whose absolute value is greater than or equal to 1 but less than 10 and the second factor is a power of 10.

And if it is a legitimate view, how do you express negative numbers in scientific notation?

  • 13
    Teacher is wrong.2012-12-07
  • 1
    Sounds like crap to me.2012-12-07
  • 3
    Your reformulation is still inadequate, as it can't express $0$.2012-12-07
  • 0
    Maybe the teacher can watch this: http://www.youtube.com/watch?v=0Elky_dDak02012-12-07
  • 0
    @ChrisEagle, does Zero exist in science? has it been measured to perfect(mathematical) precision? Don't Probabilities get just incredibly small, never 'reaching' Zero.2013-01-20
  • 0
    @ElementsinSpace Yes it does. Don't you know?2015-09-25
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    @ChrisEagle: when do you need to write $0$ in the scientific notation ? And with what exponent ?2015-09-25
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    @YvesDaoust you can express zero in scientific notation as $ 0 \times 10^0 $ if you really want to use scientific notation.2016-05-22
  • 0
    @WarrenHill: this doesn't answer my question to ChrisEagle.2016-05-24
  • 0
    @YvesDaoust one situation where I have wanted zero in scientific notation was as part of an engineering test setup where results were logged to a PC. Having all results in scscientific notation made getting results easier to parse. Zero was +0.0000E+002016-05-24

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