# 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?

Jul 8, 2017

$0.238$ $\text{L}$ = 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

$0.238$ $\text{L}$

The conversion factor is

$1$ $\text{gal}$ $= 3.785$ $\text{L}$

which we can also write as

$\left(1 \textcolor{w h i t e}{l} \text{gal")/(3.785color(white)(l)"L}\right)$

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, $0.238$ $\text{L}$ is equal to

$\textcolor{red}{\underline{0.0629 \textcolor{w h i t e}{l} \text{gal}}}$