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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].
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].
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