Sure, let's walk through the division step-by-step and express the result in scientific notation.
We are given the following operation to perform:
[tex]\[
\frac{6.900 \times 10^{10}}{4.000 \times 10^{8}}
\][/tex]
### Step 1: Divide the Coefficients
First, divide the coefficients [tex]\(6.900\)[/tex] by [tex]\(4.000\)[/tex]:
[tex]\[
6.900 \div 4.000 = 1.725
\][/tex]
### Step 2: Subtract the Exponents
Next, we handle the powers of 10. When you divide powers of ten, you subtract the exponent of the denominator from the exponent of the numerator:
[tex]\[
10^{10} \div 10^{8} = 10^{10 - 8} = 10^{2}
\][/tex]
### Step 3: Combine the Results
Now, we combine the result of the coefficient division with the result of the exponent subtraction:
[tex]\[
1.725 \times 10^{2}
\][/tex]
### Final Answer
Expressing the result in correct scientific notation:
[tex]\[
1.725 \times 10^{2}
\][/tex]
Hence, the result of the operation [tex]\(\frac{6.900 \times 10^{10}}{4.000 \times 10^{8}}\)[/tex] is:
[tex]\[
1.725 \times 10^{2}
\][/tex]
