Which of the following is the correct conversion of 0.00781 g to kilograms (kg)?

• A. 7.81 × 10^{-5} kg
• B. 7.81 × 10^{-6} kg
• C. 7.81 × 10^{-4} kg
• D. 7.81 × 10^{-3} kg

Answer: (B)

Verified step by step guidance

1. Recall the relationship between grams and kilograms: 1 kilogram (kg) is equal to 1000 grams (g), or mathematically, \$1\,\text{kg} = 10^{3}\,\text{g}$.
2. To convert grams to kilograms, divide the mass value in grams by 1000, which is the same as multiplying by \$10^{-3}\(: \)\text{mass in kg} = \text{mass in g} \times 10^{-3}$.
3. Apply this conversion to the given mass: \$0.00781\,\text{g} \times 10^{-3} = 0.00781 \times 10^{-3}\,\text{kg}$.
4. Express the result in scientific notation by moving the decimal point appropriately: \$0.00781 = 7.81 \times 10^{-3}\(, so multiply this by \)10^{-3}\( to get \)7.81 \times 10^{-3} \times 10^{-3} = 7.81 \times 10^{-6}$.
5. Therefore, the correct conversion of 0.00781 g to kilograms is \$7.81 \times 10^{-6}\,\text{kg}$.