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.
$$-4 \times 10^{50}$$
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?
Best Answer
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.