Divide [tex]\(\frac{3.185 \times 10^{17}}{9.1 \times 10^8}\)[/tex]. Write the final answer in scientific notation.

A. [tex]\(3.5 \times 10^8\)[/tex]

B. [tex]\(0.35 \times 10^9\)[/tex]

C. [tex]\(3.5 \times 10^9\)[/tex]

D. [tex]\(0.35 \times 10^{25}\)[/tex]



Answer :

To divide numbers in scientific notation, we follow these steps:

1. Divide the coefficients: Divide [tex]\(3.185\)[/tex] by [tex]\(9.1\)[/tex].
2. Subtract the exponents: Subtract the exponent in the denominator from the exponent in the numerator.

Let's go through the steps in detail:

1. Divide the coefficients:
[tex]\[ \frac{3.185}{9.1} \approx 0.35 \][/tex]

2. Subtract the exponents:
[tex]\[ 17 - 8 = 9 \][/tex]

So the division of the scientific notation yields:
[tex]\[ 0.35 \times 10^9 \][/tex]

However, we usually aim to write the result in standard scientific notation, where the coefficient is between 1 and 10. To do this, we adjust [tex]\(0.35 \times 10^9\)[/tex] as follows:

[tex]\[ 0.35 \times 10^9 = 3.5 \times 10^8 \][/tex]

Thus, the correct answer in standard scientific notation is:
[tex]\[ 3.5 \times 10^8 \][/tex]

Therefore, the correct choice from the given options is:
[tex]\[ \boxed{3.5 \times 10^8} \][/tex]