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Perform the following operation and express the answer in correct scientific notation.

[tex]\[
3.8 \times 10^{-5} \div 8.1 \times 10^3
\][/tex]

[tex]\[
[?] \times 10^{[?]}
\][/tex]


Sagot :

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]