Units of Capacity (Gallon and Fluid Ounce)
Ximena is traveling with her family to San Antonio, Texas. At a gas station she sees a sign: "3.50 dollars per gallon." In Mexico, her dad pays by the liter. Where is gasoline cheaper? To find out, we first need to understand how capacity is measured in each system and how to convert from one to the other. We'll solve it at the end of the page.
Capacity in the International System
Capacity is the amount of liquid that fits in a container. In Mexico we measure it in liters (L) and milliliters (mL). A water jug is 20 L and a bottle of soda is 600 mL.
Why? A cube that is 10 cm on each side has a volume of $10 \times 10 \times 10 = 1000 \text{ cm}^3$ and is a cubic decimeter: it holds 1000 mL, which is 1 L. And a cubic meter is $10 \times 10 \times 10 = 1000$ of those cubes, that is, 1000 L.
A large soft drink from the United States contains 32 fluid ounces. If $1 \text{ fluid ounce} = 29.57 \text{ mL}$, how many milliliters does it contain? And…
A large soft drink from the United States contains 32 fluid ounces. If $1 \text{ fluid ounce} = 29.57 \text{ mL}$, how many milliliters does it contain? And approximately how many liters?
Gallon and fluid ounce
In the United States, liquids are measured in gallons (gal) and fluid ounces (fl oz). You'll see them on gasoline, milk, and soda there.
These are approximate values. To get a feel for them: a gallon is a little less than 4 liters, and a fluid ounce is about two tablespoons (around 30 mL), since a tablespoon is about 15 mL.
There is another relationship between them: $1 \text{ gal} = 128 \text{ fl oz}$.
A bucket has a capacity of 4 gallons. How many liters is that? Use $1 \text{ gallon} = 3.785 \text{ L}$.
A bucket has a capacity of 4 gallons. How many liters is that? Use $1 \text{ gallon} = 3.785 \text{ L}$.
Converting with conversion factors
A conversion factor is a fraction equal to 1 that has the same quantity written in two units, for example $\dfrac{3.785 \text{ L}}{1 \text{ gal}}$. Multiplying by it changes the unit without changing the quantity. You set it up so that the unit you want to get rid of is on the bottom and cancels out.
At a gas station in the United States, a car's tank holds 12 gallons. How many liters of gasoline fit? Use $1 \text{ gallon} = 3.785 \text{ L}$ and round to the nearest…
At a gas station in the United States, a car's tank holds 12 gallons. How many liters of gasoline fit? Use $1 \text{ gallon} = 3.785 \text{ L}$ and round to the nearest tenth.
Changes within the same system and large results
Sometimes you need to use two factors in a row. For example, a pool of 500 gallons, how many cubic meters is that?
For the soda example: $32 \text{ fl oz} \times 29.57 = 946.24 \text{ mL}$, which is $0.94624 \text{ L}$, almost 1 liter.
A small pool needs 500 gallons of water to fill. How many liters are required? Express the result also in cubic meters (remember that $1000 \text{ L} = 1 \text{ m}^3$).
A small pool needs 500 gallons of water to fill. How many liters are required? Express the result also in cubic meters (remember that $1000 \text{ L} = 1 \text{ m}^3$).
Comparing prices in different units
To compare, everything must be in the same unit. Let's answer Ximena's question.
Back to the beginning: in San Antonio, gasoline costs Ximena about $\$16.64$ per liter, cheaper than in Mexico.
In the United States, gasoline costs 3.50 dollars per gallon. In Mexico it costs $\$24.50$ per liter. If $1 \text{ gallon} = 3.785 \text{ L}$ and $1 \text{ dollar} =…
In the United States, gasoline costs 3.50 dollars per gallon. In Mexico it costs $\$24.50$ per liter. If $1 \text{ gallon} = 3.785 \text{ L}$ and $1 \text{ dollar} = \$18$ pesos, in which country is gasoline cheaper per liter?
Summary
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SI equivalences: $1 \text{ L} = 1000 \text{ mL}$, $1 \text{ m}^3 = 1000 \text{ L}$, $1 \text{ dm}^3 = 1 \text{ L}$, $1 \text{ cm}^3 = 1 \text{ mL}$.
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US customary system: $1 \text{ gal} = 3.785 \text{ L}$ and $1 \text{ fl oz} = 29.57 \text{ mL}$.
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To go from gallons to liters, multiply by 3.785; to go from liters to gallons, divide.
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The conversion factor is set up so that the unit you want to get rid of cancels out.
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To compare prices, convert everything to the same currency and the same unit.