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?

1 Answer
Jul 8, 2017

Answer:

#0.238# #"L"# #= color(red)(0.0629# #color(red)("gal"#

Explanation:

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

#0.238# #"L"#

The conversion factor is

#1# #"gal"# #= 3.785# #"L"#

which we can also write as

#(1color(white)(l)"gal")/(3.785color(white)(l)"L")#

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:

#0.238cancel("L")((1color(white)(l)"gal")/(3.785cancel("L"))) = color(red)(0.0629# #color(red)("gal"#

Therefore, #0.238# #"L"# is equal to

#color(red)(ul(0.0629color(white)(l)"gal"))#