Question

which of the following values are between $5 \times 10^{-4}$ and $2 \times 10^{-3}$? choose all that apply.
$4 \times 10^{-4}$ $7 \times 10^{-4}$ $9 \times 10^{-4}$ $1 \times 10^{-3}$ $3 \times 10^{-3}$ $5 \times 10^{-3}$

Explanation:

Step1: Convert to same exponent

Rewrite \(2 \times 10^{-3}\) as \(20 \times 10^{-4}\), and \(1 \times 10^{-3}\) as \(10 \times 10^{-4}\). The range becomes \(5 \times 10^{-4}\) to \(20 \times 10^{-4}\).

Step2: Compare each value

• \(4 \times 10^{-4}\): \(4 < 5\) → outside range
• \(7 \times 10^{-4}\): \(5 < 7 < 20\) → inside range
• \(9 \times 10^{-4}\): \(5 < 9 < 20\) → inside range
• \(10 \times 10^{-4}\) (\(1 \times 10^{-3}\)): \(5 < 10 < 20\) → inside range
• \(3 \times 10^{-3} = 30 \times 10^{-4}\): \(30 > 20\) → outside range
• \(5 \times 10^{-3} = 50 \times 10^{-4}\): \(50 > 20\) → outside range

Answer:

\(7 \times 10^{-4}\), \(9 \times 10^{-4}\), \(1 \times 10^{-3}\)