A coffee cup is found to have a volume of 0.238 liters. How do you calculate, using unit analysis, the volume of the coffee cup, in gallons?
Using dimensional analysis, we can multiply the known value by a conversion factor to convert to a new unit while canceling the old one.
The known value here is
The conversion factor is
which we can also write as
We multiply the conversion factor by the known value so that the units cancel out algebraically and you're left with the desired unit. It looks like this: