To convert milligrams to kilograms, which conversion factors would you need? \frac{1g}{1,000 mg} and \frac{1 kg}{1,000 g} \frac{1g}{1,000 mg} and \frac{1g}{1,000 kg} \frac{1 mg}{100 g} and \frac{1,000 g}{1 kg} \frac{100 mg}{1g} and \frac{1,000 g}{1 kg}
The Correct Answer and Explanation is:
The correct conversion factors to use when converting milligrams to kilograms are:
1g1,000mgand1kg1,000g\frac{1g}{1,000 mg} \quad \text{and} \quad \frac{1 kg}{1,000 g}
Explanation:
When converting milligrams (mg) to kilograms (kg), the process involves two steps: converting milligrams to grams and then grams to kilograms.
- Step 1: Convert milligrams to grams We know that 1 gram (g) is equivalent to 1,000 milligrams (mg). This means the conversion factor to go from milligrams to grams is:
1g1,000mg\frac{1g}{1,000 mg}
Using this factor, if we have xx mg, we multiply by 1g1,000mg\frac{1g}{1,000 mg}, effectively dividing by 1,000 to get grams.
- Step 2: Convert grams to kilograms We also know that 1 kilogram (kg) is equivalent to 1,000 grams (g). So, the conversion factor to go from grams to kilograms is:
1kg1,000g\frac{1 kg}{1,000 g}
If we have yy grams, we multiply by 1kg1,000g\frac{1 kg}{1,000 g}, effectively dividing by 1,000 to get kilograms.
Full Conversion Process:
Now, applying both conversion factors together:
x mg×1g1,000mg×1kg1,000gx \text{ mg} \times \frac{1g}{1,000 mg} \times \frac{1 kg}{1,000 g}
Since multiplying fractions means multiplying numerators and denominators, the units cancel out, leaving:
x1,000,000 kg\frac{x}{1,000,000} \text{ kg}
This means to convert milligrams to kilograms, you simply divide the milligram value by 1,000,000.
Why This Works:
Each step systematically moves between metric units using known relationships, ensuring accurate conversion. Using incorrect factors would result in incorrect unit cancellation or scaling errors. The selected conversion factors ensure proper unit transition from milligrams to grams and then kilograms correctly.
