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Which expression is equivalent to 0.0000981?

A. [tex]98.1 \times 10^{-5}[/tex]
B. [tex]9.81 \times 10^{-6}[/tex]
C. [tex]9.81 \times 10^5[/tex]
D. [tex]9.81 \times 10^{-5}[/tex]

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].

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