To perform the operation [tex]\( \frac{3.8 \times 10^{-5}}{8.1 \times 10^3} \)[/tex] and express the answer in correct scientific notation, we will follow these steps:
### Step 1: Division of the Coefficients
First, we divide the base numbers (coefficients):
[tex]\[
\frac{3.8}{8.1} \approx 0.4691358024691358
\][/tex]
### Step 2: Subtraction of the Exponents
Next, we handle the exponents. When we divide numbers in scientific notation, we subtract the exponent in the denominator from the exponent in the numerator:
[tex]\[
-5 - 3 = -8
\][/tex]
### Step 3: Combine the Result
Combining the results from steps 1 and 2,
[tex]\[
\frac{3.8 \times 10^{-5}}{8.1 \times 10^3} \approx 0.4691358024691358 \times 10^{-8}
\][/tex]
### Step 4: Adjust to Scientific Notation
Scientific notation requires a number between 1 and 10 (1 ≤ number < 10) for the coefficient. Therefore, we need to adjust 0.4691358024691358 to fit this requirement:
[tex]\[
0.4691358024691358 = 4.6913580246913575 \times 10^{-1}
\][/tex]
When we adjust the number to [tex]\(4.6913580246913575 \times 10^{-1}\)[/tex] in scientific notation, we must also adjust the exponent accordingly. Therefore, we add [tex]\(-1\)[/tex] to the previously calculated exponent [tex]\(-8\)[/tex]:
[tex]\[
-8 - 1 = -9
\][/tex]
### Final Answer
Thus, the final result expressed in correct scientific notation is:
[tex]\[
4.6913580246913575 \times 10^{-9}
\][/tex]
So,
[tex]\[
\frac{3.8 \times 10^{-5}}{8.1 \times 10^3} = 4.6913580246913575 \times 10^{-9}
\][/tex]
