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. Write the division in fractional form:
[tex]\[
\frac{3.14 \times 10^{-2}}{2.65 \times 10^{-7}}
\][/tex]
2. Separate the coefficients and the powers of 10:
[tex]\[
= \frac{3.14}{2.65} \times \frac{10^{-2}}{10^{-7}}
\][/tex]
3. Divide the coefficients:
[tex]\[
\frac{3.14}{2.65} \approx 1.18
\][/tex]
4. Subtract the exponents in the powers of 10:
[tex]\[
10^{-2 - (-7)} = 10^{-2 + 7} = 10^{5}
\][/tex]
5. Combine the coefficient and the power of 10:
[tex]\[
1.18 \times 10^{5}
\][/tex]
Thus, the answer in correct scientific notation is:
[tex]\[
1.18 \times 10^{5}
\][/tex]
