Question

multiply, expressing the product in scientific notation.
\\((9.16 \times 10^{-3})(5.5 \times 10^{10})\\)

\\(5.038 \times 10^{8}\\)
\\(5.038 \times 10^{-12}\\)
\\(50.38 \times 10^{7}\\)
\\(5.038 \times 10^{6}\\)

Explanation:

Group the factors

Using the Product of Powers Rule knowledge point

$$ (9.16 \times 10^{-3})(5.5 \times 10^{10}) = (9.16 \times 5.5) \times (10^{-3} \times 10^{10}) $$

Multiply the decimal coefficients

Multiply the numerical coefficients:

$$ 9.16 \times 5.5 = 50.38 $$

Multiply the powers of ten

Using the Product of Powers Rule knowledge point

$$ 10^{-3} \times 10^{10} = 10^{-3 + 10} = 10^7 $$

Combine and normalize to scientific notation

Combine the parts:

$$ 50.38 \times 10^7 $$

Convert to standard scientific notation where the coefficient is between \(1\) and \(10\):

$$ 50.38 \times 10^7 = (5.038 \times 10^1) \times 10^7 = 5.038 \times 10^8 $$

Answer:

• (A) \(5.038 \times 10^8\) (Correct answer)
• (B) \(5.038 \times 10^{-12}\)
• (C) \(50.38 \times 10^7\)
• (D) \(5.038 \times 10^6\)