Question

you are asked to convert 37.5 milligrams (mg) into grams. how would you properly set-up the conversion?

• divide 37.5 mg by 10,000
• multiply 37.5 mg by 1000 mg/g
• multiply 37.5 mg by 1000g/mg
• divide 37.5 mg by 100
• multiply 37.5 mg by 1 g/1000 mg

Explanation:

To convert milligrams to grams, we use the conversion factor \(1\space g = 1000\space mg\), which can be written as \(\frac{1\space g}{1000\space mg}\). To convert \(37.5\space mg\) to grams, we multiply by this conversion factor so that the milligram units cancel out, leaving grams. Let's analyze each option:

• Dividing by 10,000 is incorrect as the conversion between mg and g is a factor of 1000, not 10,000.
• Multiplying by \(1000\space mg/g\) would give units of \(mg^2/g\), which is not grams.
• Multiplying by \(1000\space g/mg\) is incorrect as it would result in an extremely large number and wrong units.
• Dividing by 100 is incorrect as the conversion factor is 1000, not 100.
• Multiplying by \(\frac{1\space g}{1000\space mg}\) is correct because when we multiply \(37.5\space mg\times\frac{1\space g}{1000\space mg}\), the \(mg\) units cancel and we get the value in grams.

Answer:

Multiply 37.5 mg by 1 g/1000 mg