A small sample of osmium was found to have a mass of 22.6 grams. What is that value in kilograms?
In order to answer this question, we will need to use dimensional analysis. Dimensional analysis is a problem-solving method used to convert between two units, whereby the original value is multiplied by a conversion factor or several conversion factors if necessary. We know from the question that the original value is 22.6 grams, but we don’t yet know which conversion factor to use.
A conversion factor is a relationship of two equal quantities that have different units. 60 seconds is equal to one minute is an example of a conversion factor. For this question, we need to determine the conversion factor that relates the units grams and kilograms. The prefix kilo- gives us a clue. Kilo- means 1000, so a kilogram is equal to 1000 grams. In order to use a conversion factor in dimensional analysis, we will need to rewrite the conversion factor as a fraction. Thus, we could write this relationship as one kilogram per 1000 grams or 1000 grams per one kilogram, where the symbol kg represents the unit kilogram.
But which conversion factor do we use for this dimensional analysis problem? We should recognize that when multiplying or dividing, units will cancel when they appear in both the numerator and the denominator. Our original value has the unit grams. This unit appears in the numerator. In order for the unit grams to cancel, the unit gram will also need to appear in the denominator. Therefore, we should choose the representation of the conversion factor that has the unit grams in the denominator.
We can then multiply the original value by our chosen conversion factor. The gram unit will cancel, leaving us with the unit kilograms. We perform the calculation and determine that a sample of osmium with a mass of 22.6 grams will also have a mass of 0.0226 kilograms.