To solve the given problem [tex]\(\frac{3.8 \times 10^{-5}}{8.1 \times 10^3}\)[/tex] and express the answer in scientific notation, let's proceed with the following steps:
1. Understand the Operation:
We need to divide [tex]\(3.8 \times 10^{-5}\)[/tex] by [tex]\(8.1 \times 10^3\)[/tex].
2. Combine Coefficients and Powers Separately:
When dividing two numbers in scientific notation, we divide their coefficients (the numbers in front of the powers of 10) and subtract the exponents.
[tex]\[
\frac{3.8 \times 10^{-5}}{8.1 \times 10^3} = \left(\frac{3.8}{8.1}\right) \times 10^{-5 - 3}
\][/tex]
3. Calculate the Coefficient:
Divide the coefficients:
[tex]\[
\frac{3.8}{8.1} \approx 0.4691358024691358
\][/tex]
4. Calculate the Power of 10:
Subtract the exponents:
[tex]\[
10^{-5 - 3} = 10^{-8}
\][/tex]
So, combining these results, we have:
[tex]\[
0.4691358024691358 \times 10^{-8}
\][/tex]
5. Express Result in Proper Scientific Notation:
Scientific notation requires the coefficient to be between 1 and 10. We adjust the coefficient and exponent accordingly:
[tex]\[
0.4691358024691358 = 4.6913580246913575 \times 10^{-1}
\][/tex]
Thus, we adjust the exponent:
[tex]\[
4.6913580246913575 \times 10^{-1} \times 10^{-8} = 4.6913580246913575 \times 10^{-9}
\][/tex]
Therefore, the result of [tex]\(\frac{3.8 \times 10^{-5}}{8.1 \times 10^3}\)[/tex] is:
[tex]\[
4.6913580246913575 \times 10^{-9}
\][/tex]
So, the final answer in scientific notation is:
[tex]\[
4.6913580246913575 \times 10^{-9}
\][/tex]
