How many ‘kilograms are in 452 mg? 4.52 x 10-7 kg 4.52 x 10-4 kg 0.452 kg 4.52 * 108 kg
The Correct Answer and Explanation is:
To convert 452 milligrams (mg) to kilograms (kg), we need to understand the relationship between these units:
- 1 kilogram (kg) = 1,000,000 milligrams (mg)
This means:
1 mg=1×10−6 kg1 \, \text{mg} = 1 \times 10^{-6} \, \text{kg}1mg=1×10−6kg
Step-by-step calculation:
452 mg=452×10−6 kg452 \, \text{mg} = 452 \times 10^{-6} \, \text{kg}452mg=452×10−6kg
Now simplify the expression:452×10−6=4.52×10−4 kg452 \times 10^{-6} = 4.52 \times 10^{-4} \, \text{kg}452×10−6=4.52×10−4kg
Final Answer:
4.52 × 10⁻⁴ kg
Explanation
Understanding unit conversions between milligrams and kilograms is essential, especially in fields like medicine, chemistry, and physics. The metric system is based on powers of ten, which makes conversions relatively straightforward once the relationships between units are understood. In this case, we are converting 452 milligrams (mg) into kilograms (kg).
The key is to remember how many milligrams are in a kilogram. There are 1,000 grams in a kilogram and 1,000 milligrams in a gram. Therefore, there are 1,000 × 1,000 = 1,000,000 milligrams in one kilogram. This is the same as saying:1 mg=1÷1,000,000=0.000001 kg=1×10−6 kg1 \, \text{mg} = 1 \div 1,000,000 = 0.000001 \, \text{kg} = 1 \times 10^{-6} \, \text{kg}1mg=1÷1,000,000=0.000001kg=1×10−6kg
To convert milligrams to kilograms, multiply the number of milligrams by 1×10−61 \times 10^{-6}1×10−6. For 452 milligrams:452×10−6=4.52×10−4 kg452 \times 10^{-6} = 4.52 \times 10^{-4} \, \text{kg}452×10−6=4.52×10−4kg
This means that 452 mg is equal to 0.000452 kilograms, or expressed in scientific notation, 4.52 × 10⁻⁴ kg. This notation is particularly useful in scientific calculations where very large or very small numbers are involved.
The other choices given are either too large or incorrectly expressed. For example, 0.452 kg is far too large since it would be 452,000 mg, not 452 mg. Likewise, 4.52 × 10⁻⁷ kg is too small, and 4.52 × 10⁸ kg is completely off scale.
Thus, the correct and scientifically accurate answer is:
4.52 × 10⁻⁴ kilograms.
