Question

which list is in order from least to greatest?

\\(9.4 \times 10^{-8}, 9.25 \times 10^{-6}, 2.5 \times 10^{3}, 7 \times 10^{3}\\)
\\(2.5 \times 10^{3}, 7 \times 10^{3}, 9.25 \times 10^{-6}, 9.4 \times 10^{-8}\\)
\\(9.25 \times 10^{-6}, 9.4 \times 10^{-8}, 7 \times 10^{3}, 2.5 \times 10^{3}\\)
\\(9.4 \times 10^{-8}, 9.25 \times 10^{-6}, 7 \times 10^{3}, 2.5 \times 10^{3}\\)

Explanation:

Compare the exponents of the powers of 10

$$ -8 < -6 < 3 $$

Compare numbers with the same exponent

For \(10^{-8}\):

$$ 9.4 \times 10^{-8} $$

For \(10^{-6}\):

$$ 9.25 \times 10^{-6} $$

For \(10^{3}\):

$$ 2.5 < 7 \implies 2.5 \times 10^3 < 7 \times 10^3 $$

Order the complete list from least to greatest

$$ 9.4 \times 10^{-8} < 9.25 \times 10^{-6} < 2.5 \times 10^3 < 7 \times 10^3 $$

Answer:

• (A) \(9.4 \times 10^{-8}, 9.25 \times 10^{-6}, 2.5 \times 10^3, 7 \times 10^3\) (Correct answer)
• (B) \(2.5 \times 10^3, 7 \times 10^3, 9.25 \times 10^{-6}, 9.4 \times 10^{-8}\)
• (C) \(9.25 \times 10^{-6}, 9.4 \times 10^{-8}, 7 \times 10^3, 2.5 \times 10^3\)
• (D) \(9.4 \times 10^{-8}, 9.25 \times 10^{-6}, 7 \times 10^3, 2.5 \times 10^3\)