Sure, let's perform the operation [tex]\( \frac{6.900 \times 10^{10}}{4.000 \times 10^8} \)[/tex] step-by-step and express the answer in scientific notation.
1. Divide the coefficients:
[tex]\[ \frac{6.900}{4.000} = 1.725 \][/tex]
2. Subtract the exponents:
[tex]\[ 10^{10} \div 10^8 = 10^{(10 - 8)} = 10^2 \][/tex]
Now we combine the results from step 1 and step 2:
[tex]\[ 1.725 \times 10^2 \][/tex]
Next, we need to adjust the coefficient so that it falls between 1 and 10 by expressing it correctly in scientific notation.
However, 1.725 is already in the range [1, 10), so we don't need any further adjustment of the coefficient itself.
Therefore, our result can be simplified to:
[tex]\[ 17.25 \times 10 \][/tex]
Express this in standard scientific notation:
[tex]\[ 1.725 \times 10^3 \][/tex]
Thus, the answer to the operation [tex]\( \frac{6.900 \times 10^{10}}{4.000 \times 10^8} \)[/tex] in scientific notation is:
[tex]\[ 1.725 \times 10^3 \][/tex]
So the final result is:
[tex]\[ 17.25 \times 10^3 \][/tex]
