To convert the number [tex]\(0.00000797\)[/tex] into scientific notation:
1. Identify the coefficient: The coefficient is the part of the number that is between 1 and 10. We need to express [tex]\(0.00000797\)[/tex] in the form [tex]\(a \times 10^n\)[/tex], where [tex]\(1 \leq a < 10\)[/tex].
2. Determine the coefficient: In this case, moving the decimal place to the right and making sure the result is between 1 and 10, the coefficient will be [tex]\(7.97\)[/tex].
3. Determine the exponent [tex]\( n \)[/tex]:
- Start with the original number: [tex]\(0.00000797\)[/tex].
- Count the number of places we move the decimal point to transform the number to the coefficient [tex]\(7.97\)[/tex].
- Moving the decimal point 6 places to the right transforms [tex]\(0.00000797\)[/tex] into [tex]\(7.97\)[/tex].
The number of moves determines the exponent [tex]\(n\)[/tex]. Since we moved the decimal point to the right by 6 places, the exponent [tex]\(n\)[/tex] is [tex]\(-6\)[/tex] (negative because the original number is less than 1).
Therefore, the scientific notation of [tex]\(0.00000797\)[/tex] is [tex]\(7.97 \times 10^{-6}\)[/tex], and the value of [tex]\(n\)[/tex] is [tex]\(-6\)[/tex].
The correct answer is [tex]\( \mathbf{n = -6} \)[/tex].
