To solve the given operation and express the answer in scientific notation, we need to perform the division [tex]\(3.8 \times 10^{-5} \div 8.1 \times 10^3\)[/tex]. Here's a step-by-step solution to this problem.
### Step 1: Write the given numbers in standard form
- [tex]\(3.8 \times 10^{-5}\)[/tex] in standard form is [tex]\(0.000038\)[/tex].
- [tex]\(8.1 \times 10^3\)[/tex] in standard form is [tex]\(8100\)[/tex].
### Step 2: Perform the division
[tex]\[
0.000038 \div 8100
\][/tex]
This division gives us [tex]\(4.691358024691358 \times 10^{-9}\)[/tex] in scientific notation.
### Step 3: Express the result in scientific notation
To represent the result [tex]\(4.691358024691358 \times 10^{-9}\)[/tex] in proper scientific notation:
- The coefficient (or mantissa) part is [tex]\(4.691358024691358\)[/tex].
- The exponent is [tex]\(-9\)[/tex].
For simplicity and to keep it in standard format:
- We can round the coefficient to two decimal places, making it [tex]\(4.69\)[/tex].
- Retain the exponent as it is.
### Step 4: Combine the coefficient and exponent
Therefore, the final answer in scientific notation is:
[tex]\[
4.69 \times 10^{-9}
\][/tex]
So the operation [tex]\(3.8 \times 10^{-5} \div 8.1 \times 10^3\)[/tex] results in:
[tex]\[
\boxed{4.69 \times 10^{-9}}
\][/tex]
