Question

6.2 scientific notation quiz

simplify: \\((5 \times 10^6) (5 \times 10^7)\\)

\\(2.5 \times 10^{12}\\)
\\(2.5 \times 10^{14}\\)
\\(25 \times 10^{12}\\)
\\(25 \times 10^{13}\\)

Explanation:

Group the coefficients and powers of ten

Using the Scientific Notation Multiplication knowledge point

$$ (5 \times 10^6)(5 \times 10^7) = (5 \times 5) \times (10^6 \times 10^7) $$

Multiply the coefficients

Using the Scientific Notation Multiplication knowledge point

$$ 5 \times 5 = 25 $$

Multiply the powers of ten

Using the Properties of Exponents knowledge point

$$ 10^6 \times 10^7 = 10^{6+7} = 10^{13} $$

Combine and convert to standard scientific notation

Using the Scientific Notation Multiplication knowledge point

$$
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$$

Answer:

• (A) \(2.5 \times 10^{12}\)
• (B) \(2.5 \times 10^{14}\) (Correct answer)
• (C) \(25 \times 10^{12}\)
• (D) \(25 \times 10^{13}\)