To solve the problem [tex]\( \frac{2.36 \times 10^{-2}}{8.4 \times 10^2} \)[/tex] and express the answer in scientific notation, let's break down the steps.
1. Calculate the division of the coefficients:
[tex]\[
\frac{2.36}{8.4} = 0.2809523809523809
\][/tex]
2. Subtract the exponents in the powers of ten:
[tex]\[
10^{-2} \div 10^2 = 10^{-2-2} = 10^{-4}
\][/tex]
3. Combine the results:
[tex]\[
0.2809523809523809 \times 10^{-4}
\][/tex]
4. Convert the coefficient into standard scientific notation:
Scientific notation requires that the coefficient be between 1 and 10. Currently, [tex]\( 0.2809523809523809 \)[/tex] is not in the correct form, so we need to adjust it. We can multiply [tex]\( 0.2809523809523809 \)[/tex] by [tex]\( 10 \)[/tex] to shift the decimal place and then adjust the exponent accordingly:
[tex]\[
0.2809523809523809 \times 10^{-4} = 2.809523809523809 \times 10^{-5}
\][/tex]
Therefore, the answer in correct scientific notation is:
[tex]\[
2.809523809523809 \times 10^{-5}
\][/tex]
