Scientific Notation As A Decimal 1

Yes.

But memorizing a rule, and understaning a rule are different things.
 
harpazo said:
What rule did I memorize?
Click to expand...
I think Jeff is talking about the rule for shifting the decimal point, when multiplying by a power of 10. Sometimes, people learn to manipulate symbols without really knowing why the steps are valid. We want to be sure you understand why that shifting rule works.

?
 
harpazo said:
What rule did I memorize?
Click to expand...
As otis said, I am concerned that you understand why moving the decimal point works as a purely mechanical rule, but I am also concerned that you understand the uncertainty implied by scientific notation. The explanation that you copied gives neither any mathematical justification nor any indication that scientific notation carries very useful extra-mathematical information.

[MATH]y = 9.7 \times 10^3 \implies 9600 \le y \le 9800.[/MATH]
It is arithmetically correct in pure mathematics to say

[MATH]6.7 *10^3 = 6700.[/MATH]
But in the applied mathematics implicit in scientific notation, it would be better to say

[MATH]6.7 \times 10^3 = 6700 \pm 100[/MATH]
to avoid losing valuable information.
 
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