To solve the problem [tex]\( \frac{3.14 \times 10^{-2}}{2.65 \times 10^{-7}} \)[/tex] and express the answer in scientific notation, we can follow these steps:
1. Separate the Coefficients and Powers of 10:
[tex]\[
\frac{3.14 \times 10^{-2}}{2.65 \times 10^{-7}} = \frac{3.14}{2.65} \times \frac{10^{-2}}{10^{-7}}
\][/tex]
2. Divide the Coefficients:
[tex]\[
\frac{3.14}{2.65} \approx 1.1849056603773587
\][/tex]
3. Divide the Powers of 10:
[tex]\[
\frac{10^{-2}}{10^{-7}} = 10^{-2 - (-7)} = 10^{-2 + 7} = 10^5
\][/tex]
4. Combine the Results:
[tex]\[
1.1849056603773587 \times 10^5
\][/tex]
5. Express the Final Answer in Correct Scientific Notation:
The result from the operation is [tex]\( 118490.56603773586 \)[/tex], which can be written in scientific notation as [tex]\( 1.1849056603773587 \times 10^5 \)[/tex].
Therefore, the answer to the operation [tex]\(\frac{3.14 \times 10^{-2}}{2.65 \times 10^{-7}}\)[/tex] expressed in scientific notation is:
[tex]\[
1.1849056603773587 \times 10^5
\][/tex]
