Answer :
To determine which expression is equivalent to 0.0000981, we need to convert this decimal into a form that matches one of the options provided. We'll do this by using scientific notation, which expresses numbers as a product of a number between 1 and 10 and a power of 10.
Here's a step-by-step explanation of how to match 0.0000981 to one of the options:
1. Convert 0.0000981 to Scientific Notation:
- Start with the decimal 0.0000981.
- Move the decimal point to the right until you have a number between 1 and 10. In this case, move the decimal 5 places to the right: 9.81.
- Since we moved the decimal point 5 places to the right, we multiply by 10 raised to the negative power of the number of moves: [tex]\(10^{-5}\)[/tex].
Thus, 0.0000981 is equivalent to [tex]\(9.81 \times 10^{-5}\)[/tex].
2. Review the Options:
- [tex]\(98.1 \times 10^{-5}\)[/tex]
- [tex]\(9.81 \times 10^{-6}\)[/tex]
- [tex]\(9.81 \times 10^{5}\)[/tex]
- [tex]\(9.81 \times 10^{-5}\)[/tex]
3. Compare with Converted Value:
- We determined that 0.0000981 is [tex]\(9.81 \times 10^{-5}\)[/tex].
Therefore, the expression equivalent to 0.0000981 is [tex]\(9.81 \times 10^{-5}\)[/tex].
Here's a step-by-step explanation of how to match 0.0000981 to one of the options:
1. Convert 0.0000981 to Scientific Notation:
- Start with the decimal 0.0000981.
- Move the decimal point to the right until you have a number between 1 and 10. In this case, move the decimal 5 places to the right: 9.81.
- Since we moved the decimal point 5 places to the right, we multiply by 10 raised to the negative power of the number of moves: [tex]\(10^{-5}\)[/tex].
Thus, 0.0000981 is equivalent to [tex]\(9.81 \times 10^{-5}\)[/tex].
2. Review the Options:
- [tex]\(98.1 \times 10^{-5}\)[/tex]
- [tex]\(9.81 \times 10^{-6}\)[/tex]
- [tex]\(9.81 \times 10^{5}\)[/tex]
- [tex]\(9.81 \times 10^{-5}\)[/tex]
3. Compare with Converted Value:
- We determined that 0.0000981 is [tex]\(9.81 \times 10^{-5}\)[/tex].
Therefore, the expression equivalent to 0.0000981 is [tex]\(9.81 \times 10^{-5}\)[/tex].
