To find the best estimate for [tex]\((6.3 \times 10^{-2})(9.9 \times 10^{-3})\)[/tex] written in scientific notation, let's proceed step by step.
1. Understanding the Numbers in Scientific Notation:
- [tex]\(6.3 \times 10^{-2}\)[/tex] represents the number [tex]\(0.063\)[/tex].
- [tex]\(9.9 \times 10^{-3}\)[/tex] represents the number [tex]\(0.0099\)[/tex].
2. Multiplying the Coefficients:
- Multiply [tex]\(6.3\)[/tex] by [tex]\(9.9\)[/tex]: [tex]\(6.3 \times 9.9 = 62.37\)[/tex].
3. Multiplying the Powers of 10:
- Multiply [tex]\(10^{-2}\)[/tex] by [tex]\(10^{-3}\)[/tex]: [tex]\(10^{-2} \times 10^{-3} = 10^{-5}\)[/tex].
4. Combining Steps 2 and 3:
- Combine the coefficient from step 2 with the power of 10 from step 3: [tex]\(62.37 \times 10^{-5}\)[/tex].
5. Rewriting into Proper Scientific Notation:
- Adjust the coefficient to fall between 1 and 10:
- [tex]\(62.37 \times 10^{-5}\)[/tex] can be written as [tex]\(6.237 \times 10^{-4}\)[/tex].
From the calculation steps, the result is [tex]\(6.237 \times 10^{-4}\)[/tex].
Now, let's evaluate the given options:
- [tex]\(6 \times 10^{-4}\)[/tex]
- [tex]\(60 \times 10^{-5}\)[/tex]
- [tex]\(6 \times 10^7\)[/tex]
- [tex]\(60 \times 10^6\)[/tex]
The closest estimation to [tex]\(6.237 \times 10^{-4}\)[/tex] is [tex]\(6 \times 10^{-4}\)[/tex].
Therefore, the best estimate is:
[tex]\[ 6 \times 10^{-4} \][/tex]
