Question

what is the approximate mass of a pencil?
5.0 × 10⁰ kg
5.0 × 10⁻³ kg
5.0 × 10⁻¹ kg
5.0 × 10¹ kg

Explanation:

Step1: Convert each option to grams (since 1 kg = 1000 g = \(10^3\) g)

• For \(5.0 \times 10^{0}\) kg: \(5.0\times10^{0}\text{ kg}=5.0\times10^{0}\times10^{3}\text{ g}=5.0\times10^{3}\text{ g}\) (too heavy for a pencil)
• For \(5.0 \times 10^{-3}\) kg: \(5.0\times10^{-3}\text{ kg}=5.0\times10^{-3}\times10^{3}\text{ g}=5.0\text{ g}\) (reasonable for a pencil)
• For \(5.0 \times 10^{-1}\) kg: \(5.0\times10^{-1}\text{ kg}=5.0\times10^{-1}\times10^{3}\text{ g}=5.0\times10^{2}\text{ g}=500\text{ g}\) (too heavy)
• For \(5.0 \times 10^{1}\) kg: \(5.0\times10^{1}\text{ kg}=50\text{ kg}\) (way too heavy)

Answer:

\(5.0 \times 10^{-3}\) kg