Alex K. answered • 09/25/20
U of M Chemistry PhD: College Instructor and Tutor
The question involves a conversion between SI units (metric system).
The prefix "milli" represents the factor one-thousandth, or 1/1000.
Consequently, the ratio 1000 milligrams=1 gram can be used to interconvert between one another.
Dimensional analysis uses the conversion factor to cancel out the "old unit" and maintain the "new unit."
When the same unit is present in both the denominator/numerator it cancels (just as 5/5=1, or X/X=1).
Set up the math equation as follows: 5 mg x (1g/1000mg)= ??
The milligram units will cancel, leaving only grams--which is the unit we desire.
5 mg x (1g/1000mg)= 0.005 g
Alternatively, when converting between units varying only in their prefix, it's also possible to consider "moving the decimal point" the number of places corresponding to the difference in their magnitudes.
"one-thousandth" =1/1000=0.001=10-3
You would move the decimal point 3 places to the left
