Conversion Problems in Context
Ximena's family is driving from Monterrey to San Antonio, Texas. The dashboard shows miles, the gas station charges by the gallon, and the weather is announced in degrees Fahrenheit. How do they make sense of it all in kilometers, liters, and degrees Celsius?
A Method for Any Problem
Almost all conversion problems are solved the same way: you identify which quantity each piece of data is, find its conversion factor, and multiply (or apply the formula, in the case of temperature).
These are the factors you need:
| Quantity | Equivalence |
|---|---|
| Length | $1\ \text{mi} = 1.609\ \text{km}$, $1\ \text{ft} = 0.3048\ \text{m}$, $1\ \text{in} = 2.54\ \text{cm}$ |
| Mass | $1\ \text{lb} = 0.4536\ \text{kg}$, $1\ \text{oz} = 28.35\ \text{g}$ |
| Capacity | $1\ \text{gal} = 3.785\ \text{L}$, $1\ \text{fl oz} = 29.57\ \text{mL}$ |
| Temperature | $C = \dfrac{5}{9}(F - 32)$ |
Why do we multiply? If $1\ \text{gal} = 3.785\ \text{L}$, then 2 gallons is double that: $2 \times 3.785\ \text{L}$. When going from the US customary unit to the SI unit, you multiply by the value of the equivalence. When going back, you divide.
A Mexican family travels by car to the United States. They put in 15 gallons of gasoline and drive 240 miles. Convert both figures to the International System (liters…
A Mexican family travels by car to the United States. They put in 15 gallons of gasoline and drive 240 miles. Convert both figures to the International System (liters and kilometers) to record the trip in their notebook.
Road Trips: Length and Capacity Together
On a trip to the United States, miles and gallons show up at the same time. You convert each piece of data separately, without mixing them.
Once you have both pieces of data in SI units, you can calculate the fuel efficiency, that is, the kilometers per liter: $241.35 \div 30.28 \approx 7.97\ \text{km/L}$.
Cooking and Shopping: Mass, Capacity, and Temperature
US recipes and ovens mix pounds, gallons, and degrees Fahrenheit. Temperature is different because you don't just multiply: the zero points of the two scales don't match. That is why you subtract 32 first and then multiply by $\frac{5}{9}$.
At a supermarket in the United States, Sofía buys a 14-pound turkey for dinner. The oven shows $325\,{}^{\circ}F$. Convert the turkey's weight to kilograms and the oven…
At a supermarket in the United States, Sofía buys a 14-pound turkey for dinner. The oven shows $325\,{}^{\circ}F$. Convert the turkey's weight to kilograms and the oven temperature to degrees Celsius.
A cake recipe from the United States calls for: 2 pounds of flour, 1 gallon of milk, and baking at $400\,{}^{\circ}F$ for the time needed. Convert the three figures to…
A cake recipe from the United States calls for: 2 pounds of flour, 1 gallon of milk, and baking at $400\,{}^{\circ}F$ for the time needed. Convert the three figures to the International System (grams or kilograms, liters, and degrees Celsius) so you can follow the recipe in Mexico.
Comparing Quantities: Pick a Single Unit
When one quantity is in pounds and another is in kilograms, you can't compare them directly. You convert one to the unit of the other and then compare.
Always answer the question with a sentence and with units. A number alone is not an answer.
A freight truck can carry a maximum of 10,000 pounds. It is loaded with 30 boxes weighing 80 kg each. Does it exceed the load limit? Justify your answer by converting…
A freight truck can carry a maximum of 10,000 pounds. It is loaded with 30 boxes weighing 80 kg each. Does it exceed the load limit? Justify your answer by converting the limit to kilograms using $1 \text{ pound} = 0.4536 \text{ kg}$.
Back to the beginning: Ximena's family converts miles with $1.609$, gallons with $3.785$, and degrees with $\frac{5}{9}(F-32)$, each piece of data with its own equivalence.