Question

select the correct answer.

the volume of one of the great lakes is \\(3.5 \times 10^3\\) cubic kilometers. if there are \\(6.3 \times 10^7\\) fish in the lake, what is the average number of fish per cubic kilometer?

\\(2.205 \times 10^{11}\\)
\\(1.8 \times 10^4\\)
\\(1.8 \times 10^{10}\\)
\\(2.205 \times 10^4\\)

Explanation:

Set up the division for average density

$$ \text{Average} = \frac{\text{Total Fish}}{\text{Total Volume}} = \frac{6.3 \times 10^7}{3.5 \times 10^3} $$

Divide the coefficients and subtract exponents

$$ \frac{6.3}{3.5} = 1.8 $$

$$ 10^7 \div 10^3 = 10^{7-3} = 10^4 $$

Combine into scientific notation

$$ 1.8 \times 10^4 $$

Answer:

• (A) \(2.205 \times 10^{11}\)
• (B) \(1.8 \times 10^4\) (Correct answer)
• (C) \(1.8 \times 10^{10}\)
• (D) \(2.205 \times 10^4\)