Question

A Toyota Prius hybrid gets 23 kilometers per liter in city driving. What is the mileage in miles per gallon? (Given: \(1 \mathrm{~km}=0.621 \mathrm{mi}\) and \(1 \mathrm{~L}=0.264 \mathrm{gal})\)

Short answer

The mileage is 54.10 miles per gallon.

Step-by-step solution

Identify Conversion Factors

To convert kilometers per liter to miles per gallon, use the given conversion factors: \(1 \text{ km} = 0.621 \text{ mi}\) and \(1 \text{ L} = 0.264 \text{ gal}\).

Convert Kilometers to Miles

Convert 23 kilometers to miles using the conversion factor \(1 \text{ km} = 0.621 \text{ mi}\). \[23 \text{ km} \times 0.621 \text{ mi/km} = 14.283 \text{ mi}\]

Convert Liters to Gallons

Now, convert 1 liter to gallons using the conversion factor \(1 \text{ L} = 0.264 \text{ gal}\). \[1 \text{ L} \times 0.264 \text{ gal/L} = 0.264 \text{ gal}\]

Calculate Miles Per Gallon

Now calculate the mileage in miles per gallon by dividing the miles by the gallons: \[\text{Miles per gallon} = \frac{14.283 \text{ mi}}{0.264 \text{ gal}} = 54.098 \text{ mpg}\]

Round to Appropriate Precision

Round the result to a reasonable number of significant figures. For this problem, two decimal places is appropriate: \[54.10 \text{ mpg}\]

Key concepts

Conversion Factors

When converting units, we rely on something called conversion factors. These are numbers used to change one set of units into another, by multiplying or dividing. For example, in this exercise, you need to convert kilometers per liter to miles per gallon. To do that, you use the given conversion factors:

• 1 km = 0.621 miles
• 1 liter = 0.264 gallons

These conversion factors work because they relate how much of one unit equals the other. It's like finding out how many apples equal a bunch of grapes. So, every time you need to convert, you simply multiply by the conversion factor.
To make the conversion clearer, write down what you want to convert, multiply it by the conversion factor, and voila! You have the new unit.

Mileage Calculation

Calculating mileage involves determining how far a car can travel on a certain amount of fuel. In this example, we explore this by finding out how many miles a Prius can drive on just one gallon of gas. First, we need to understand what we're starting with: the car can travel 23 kilometers on one liter of fuel.
To switch from kilometers per liter to miles per gallon, you first convert the distance from kilometers to miles (done with the conversion factor mentioned before). Next, you'll convert the liters used to gallons. Finally, to find the mileage, you divide the distance (in miles) by the amount of gas used (in gallons).
This gives you the mileage in miles per gallon, which is a common measure used in places like the United States.

Metric to Imperial Conversion

Metric to imperial conversion involves changing units of measurement from the metric system (like kilometers and liters) to the imperial system (miles and gallons). Each system has its own unique set of units.

• Metric units are scientific and universally used in most parts of the world, based on multiples of 10.
• Imperial units are a bit older and mainly used in the United States for day-to-day life.

Let's break it down. The metric system is handy for scientific purposes because of its simplicity and scalability—it easily moves up or down by tens. However, if you’re driving in the US, you'd be more familiar with miles per gallon to understand how efficient a car is.
When converting, you usually use a simple multiplication or division based on conversion factors that bridge the metric and imperial units. Like turning kilometers into miles, or liters into gallons. Pretty neat right? Once you get the hang of it, conversions are just like solving a simple math puzzle.