Question

Some time ago, a U.S. citizen traveling in Canada observed that the price of regular gasoline was 1.299 Canadian dollars per liter. The exchange rate at the time was 1.001 Canadian dollars per one U.S. dollar. Calculate the price of the Canadian gasoline in units of U.S. dollars per gallon. (Just the week before, the traveler had paid \(\$ 3.759\) per gallon in the United States.)

Short answer

The price of the Canadian gasoline in units of U.S. dollars per gallon is approximately \(4.912 \text{USD/gal}\).

Step-by-step solution

Convert the price of gasoline from Canadian dollars to U.S. dollars

To convert the price from Canadian dollars per liter to U.S. dollars per liter, divide the price in Canadian dollars by the exchange rate. The price in U.S. dollars per liter is therefore \(1.299 \text{CAD} / 1.001 \text{USD/CAD}\).

Calculate the price in U.S. dollars per liter

Perform the division from Step 1. The price in U.S. dollars per liter is \(1.299 \text{CAD} / 1.001 \text{USD/CAD} = 1.298 \text{USD/L}\). We approximated to three decimal places.

Convert liters to gallons

Since 1 U.S. gallon is equal to approximately 3.78541 liters, the price per gallon can be found by multiplying the price per liter by this conversion factor.

Calculate the price in U.S. dollars per gallon

Multiply the price in U.S. dollars per liter by the conversion factor from liters to gallons. The price per U.S. gallon is therefore \(1.298 \text{USD/L} * 3.78541 \text{L/gal} \approx 4.912 \text{USD/gal}\). We round to three significant figures.

Key concepts

Exchange Rate Calculation

Understanding exchange rate calculation is essential in today's global economy, where currency values fluctuate regularly. It's the mathematical process that helps us determine how much one currency is worth in terms of another. For example, if you're traveling abroad or making purchases from foreign businesses, you’ll likely need to convert your home currency to a foreign currency, or vice versa.

To calculate the exchange rate between two currencies, you need to know the amount of one currency that can be exchanged for a certain amount of another currency. This information is often represented as a ratio, like in our original exercise, where the exchange rate was given as 1.001 Canadian dollars (CAD) per one U.S. dollar (USD). So, to convert Canadian dollars to U.S. dollars, you would divide the amount in Canadian dollars by the exchange rate. In our example, the price of gas in U.S. dollars per liter was \[\begin{equation}1.299 \text{CAD} / 1.001 \text{USD/CAD} = 1.298 \text{USD/L}\text{.}\end{equation}\]

Keeping this process in mind is particularly handy for travelers and people doing international business, as it can significantly affect budgeting and expense calculations.

Unit Conversion Mathematics

The process of unit conversion mathematics is a fundamental skill in many fields, particularly in sciences, engineering, and everyday life scenarios like cooking or traveling. It entails converting a measurement from one unit to another. In the context of our problem, we used unit conversion to change the pricing unit from per liter to per gallon.

One common method is to use a conversion factor, which is a fraction that represents the relationship between two different units. In this case, to convert the price from liters to gallons, we use the conversion factor of 1 U.S. gallon being equivalent to approximately 3.78541 liters. Mathematically, the conversion is represented as follows: \[\begin{equation}1.298 \text{USD/L} \times 3.78541 \text{L/gal} \text{.}\end{equation}\]

By understanding unit conversion, you can easily compare quantities and prices in different units and make informed decisions. For students, mastering this technique is crucial for solving problems in various scientific subjects where different measurement systems are used.

Price Comparison Across Currencies

When we look at price comparison across currencies, it's about evaluating the cost of items or services in different monetary units. Taking the current exchange rates into account is crucial when comparing prices since they can drastically alter the perceived value.

In our exercise, we compared the price of gasoline in Canada and the United States. After converting the Canadian price to U.S. dollars, it's possible to directly compare it to the U.S. price. This comparison can reveal, for example, whether it's cheaper to purchase gas in one country over another at that specific point in time. To illustrate, our U.S. traveler found out that the price per gallon in Canada was approximately \[\begin{equation}4.912 \text{USD/gal}\end{equation}\] after conversion, which can be compared to the previous week's price in the U.S. of \[\begin{equation}3.759 \text{USD/gal}\end{equation}\].

Performing such comparisons helps in budget planning for travel, assessing potential savings, or simply understanding the purchasing power of a currency in different economic systems. It’s a valuable skill for consumers and businesses in our interconnected global market.