High School

Which of the following represents this number in scientific notation?

[tex]0.000000000386[/tex]

A. [tex]38.6 \cdot 10^{-10}[/tex]
B. [tex]3.86 \cdot 10^{11}[/tex]
C. [tex]3.86 \cdot 10^{-10}[/tex]

Answer :

To express the number [tex]\(0.000000000386\)[/tex] in scientific notation, follow these steps:

1. Identify the original number: [tex]\(0.000000000386\)[/tex].

2. Find a value between 1 and 10: We need to move the decimal point until we have a number between 1 and 10. For this number, moving the decimal point 10 places to the right gives us the number [tex]\(3.86\)[/tex].

3. Determine the exponent: Since we moved the decimal 10 places to the right, the exponent will be [tex]\(-10\)[/tex]. Moving the decimal to the right in a small number results in a negative exponent.

4. Write in scientific notation: Combine the number and the exponent derived from shifting the decimal point. The scientific notation for the number is [tex]\(3.86 \times 10^{-10}\)[/tex].

To confirm your choice among the provided options:
- [tex]\(38.6 \times 10^{-10}\)[/tex] is incorrect because after moving the decimal point, it does not match the original number [tex]\(0.000000000386\)[/tex].
- [tex]\(3.86 \times 10^{11}\)[/tex] is incorrect because it indicates a much larger number.
- [tex]\(3.86 \times 10^{-10}\)[/tex] matches exactly with our derived scientific notation.

Therefore, the correct option is [tex]\(3.86 \times 10^{-10}\)[/tex].