Which of the following conversion factors can be used to convert nanograms (ng) to milligrams (mg)?

• A. 1 mg / 1,000 ng
• B. 1,000 ng / 1 mg
• C. 1 ng / 1,000 mg
• D. 1 mg / 1,000,000 ng

Answer: (D)

Verified step by step guidance

1. Understand the relationship between the units: 1 milligram (mg) is equal to 1,000,000 nanograms (ng). This is because 1 mg = 10^{-3} grams and 1 ng = 10^{-9} grams, so the difference in scale is 10^{6}.
2. To convert from nanograms to milligrams, you need a conversion factor that cancels out nanograms and introduces milligrams. This means the conversion factor should have nanograms in the denominator and milligrams in the numerator.
3. Write the conversion factor as a fraction: \(\frac{1\ mg}{1,000,000\ ng}\). This means for every 1,000,000 nanograms, there is 1 milligram.
4. Check the other options to see if they correctly represent the relationship and cancel units properly. For example, \(\frac{1,000\ ng}{1\ mg}\) would convert milligrams to nanograms, not the other way around.
5. Use the correct conversion factor by multiplying the quantity in nanograms by \(\frac{1\ mg}{1,000,000\ ng}\) to convert to milligrams, ensuring units cancel correctly and the value is converted properly.