# Scientific notation and negative numbers

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?

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Teacher is wrong. –  mjqxxxx Dec 7 '12 at 4:53
Sounds like crap to me. –  copper.hat Dec 7 '12 at 4:56
Your reformulation is still inadequate, as it can't express $0$. –  Chris Eagle Dec 7 '12 at 8:14
Maybe the teacher can watch this: youtube.com/watch?v=0Elky_dDak0 –  Amzoti Dec 7 '12 at 9:34
@ChrisEagle, does Zero exist in science? has it been measured to perfect(mathematical) precision? Don't Probabilities get just incredibly small, never 'reaching' Zero. –  Elements in Space Jan 20 '13 at 17:23

You are right. The textbook and teacher are wrong.

Scientific notation is where numbers are written in the form $a × 10^b$ where $a ∈ ℝ$ and $b ∈ ℤ$.

Normalized scientific notation also stipulates that $1 ≤ |a| < 10$.

$\therefore \;\; -4 × 10^{50}$ is correct normalized scientific notation, as common sense would dictate.

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You would write the problem as: |-4| x 10^50, or 4x10^50. Your teacher is right, you cannot express a scientific notation as a negative number. It has to be a number greater than or equal to one, but less than 10. The absolute value would be taken, therefore, giving you 4x10^50. I just did one like this in college Chemistry. Thanks! MB

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Sorry, I'm not following what you are trying to say. –  Yishai Jan 29 at 22:33
To be more specific, I'm not seeing how you are expressing (or distinguishing) a negative. –  Yishai Jan 29 at 22:40