Back
Perform Unit Conversions for Fuel Economy
> ... Math > Unit Conversions > Perform Unit Conversions for Fuel Economy

Introduction

In this lesson, you will perform unit conversions for fuel economy. Fuel economy of vehicles compares the distance the vehicle can go compared to the amount of fuel it uses or the cost of the fuel. In this lesson, you will use unit conversion to determine the cost of a delivery.


This video illustrates the lesson material below. Watching the video is optional.


Unit Conversion for Fuel Economy

Performing unit conversions can feel tricky, but remembering three simple steps can help it feel more manageable. First, start by looking at the units that you have. Next, decide which units you want your answer to be in. Finally, find and use the correct conversion factor.

Example 1
How much does it cost to drive 15 km using a car that uses 7.8 L per 100 km when the current cost of petrol is 1.47 EUR?

You are starting in units of km, and you want to get to units of EUR.

  • You are starting with \(\frac {7.8L}{100km}\)
  • You want to end with \(\frac {? EUR}{15km}\)
  • Find and use the following unit conversion factors to calculate the answer
    • \(100 \space km=7.8 \space L\)
    • \(1 \space L=1.47 \space EUR\)
  • Knowing these two conversion factors, you can calculate the cost to drive 15 km.

To set up the equation, start with 15 km:
\begin{align*} &\frac{15km}{1} \end{align*}

You want to cancel out the units of km because you are looking for an answer in EUR, so you will use the conversion factor of \(100 \space km=7.8 \space L\). Set up this conversion factor as a fraction. Make sure the identical units are on opposite sides of the fraction from one another; in this case, the km from 15 km are on top of the first fraction, so place the 100 km on the bottom of the next fraction:

\begin{align*} &\frac{15\; \color{red}\cancel{km}}{1} \times \frac{7.8\;L}{100\;\color{red}\cancel{km}} \end{align*}

Next, you need to get from L to EUR. Thankfully, you have the conversion factor of \(1 \space L=1.47 \space EUR\). Since L is on top of the second fraction, place it on the bottom of the third fraction to cancel it out, as shown below:

\begin{align*} &\frac{15\; \color{red}\cancel{km}}{1} \times \frac{7.8\;\color{blue}\cancel{L}}{100\;\color{red}\cancel{km}} \times \frac{1.47\;EUR}{1\;\color{blue}\cancel{L}}\end{align*}

Use this zigzag pattern so that you can be sure that you multiply everything you need to multiply and divide everything you need to divide.

To solve, start by multiplying all of the numerators together:

\begin{align*}15\times7.8\times1.47=171.99\end{align*}

Next, multiply all of the numbers in the denominators together and divide the numerator by that total denominator.

\begin{align*} &\frac{15 \times 7.8 \times 1.47\;EUR}{1 \times 100 \times 1} = \frac{171.99\;EUR}{100} = 1.72\;EUR \end{align*}

The answer is rounded up to 1.72. Since the unit is in EUR, that means that it costs 1.72 EUR to drive 15km using a car that uses 7.8L per 100 km when the current cost of petrol is 1.47 EUR.


Things to Remember


  • Unit Conversion for Fuel Economy:
    1. Start with what unit you know.
    2. Determine what unit you want to get in the end to help you figure out what the end units should be.
    3. Determine what conversion factor(s) to use. You may sometimes need more than one.
    4. Multiply by 1 in the form of the conversion factor that cancels out the unwanted units.

Practice Problems

1. You are planning to go on a trip with some friends. Your vehicle gets 25 miles per gallon (mpg), and you want to drive from Los Angeles to San Francisco. San Francisco is 382 miles away. The current gas price is $3.75 per gallon. How much will the gas for your trip cost, in US Dollars? Round to the nearest penny (hundredth).
25 mi = 1 gal
$3.75 = 1 gal
(
Solution
x
Solution:
\(\displaystyle \frac{382\:\text{mi}}{1}\times\frac{1\:\text{gal}}{25\:\text{mi}}\times\frac{\$3.75}{1\:\text{gal}} = \$57.30\)

Written Solution:

Step 1: Start with what you know.

You know that it is 382 miles to San Francisco from Los Angeles.

Step 2: Determine what you want to get in the end (figure out what the end units should be):

You need to find out how much the trip will cost so the units you are looking for are US Dollars.

Step 3: Determine what conversion factor(s) to use:

25 mi = 1 gal

$3.75 = 1 gal

Step 4: Multiply by 1 in the form of the conversion factor that cancels out the unwanted units.

You are starting with 382 miles and need to find the cost of the trip, so you will multiply 382 miles by the conversion factors that will cancel out miles and gallons and leave you with dollars:

\(\displaystyle \frac{382\:\text{mi}}{1}\times\frac{1\:\text{gal}}{25\:\text{mi}}\times\frac{\$3.75}{1\:\text{gal}}\)

Note that multiplying by each of the two conversion factors, \(\dfrac{1\:\text{gal}}{25\:\text{mi}}\) and \(\dfrac{\$3.75}{1\:\text{gal}}\), is the same as multiplying by 1 since the numerator is equal to the denominator in both cases. This is why you can do unit conversions.

Then cancel out miles and gallons:

\(\displaystyle \frac{382\:\cancel{{\color{Red} \text{mi}}}}{1}\times\frac{1\:\cancel{{\color{Blue} \text{gal}}}}{25\:\cancel{{\color{Red} \text{mi}}}}\times\frac{\$3.75}{1\:\cancel{{\color{Blue} \text{gal}}}}\)

Using the zig-zag method you make the calculations in a zig-zag pattern. Remember: Any time you move to the denominator you divide. And any time you move to the numerator, you multiply the following:

The three fractions being multiplied together with arrows indicating the zig-zag method as written below.

\(382 \div 1 \times 1 \div 25 \times $3.75 \div 1 = $57.3\)

So it will cost $57.30 to drive from Los Angeles to San Francisco.
)
2. How much does it cost to drive 23 miles using a truck that takes 10 gallons to go 120 miles, if the current cost of gas is $3.55? Round to the nearest penny (hundredth).
10 gal = 120 mi
$3.55 = 1 gal
(
Solution
x
Solution:
\(\displaystyle \frac{23\:\text{mi}} {1}\times\frac{10\:\text{gal}}{120\:\text{mi}}\times\frac{\$3.55}{1\:\text{gal}} = \$6.80\)
)
3. Pam lives in the mountains far away from any power source. She uses an oil lamp to light her cabin at night. She goes through 3 ounces of oil each night. The current cost of oil is $9 per gallon. How much does it cost Pam to light her cabin each night in US Dollars? Use the following information to find the answer. Round to the nearest penny (hundredth).
$9 = 1 gal
3 oz = 1 night
1 gal = 128 oz
(
Solution
x
Solution:
\(\displaystyle \frac{3\:\text{oz}}{1\:\text{night}}\times\frac{1\:\text{gal}}{128\:\text{oz}}\times\frac{\$9}{1\:\text{gal}}= \$0.21\)

Written Solution:

Step 1: Start with what you know.

You know that Pam uses 3 ounces of oil per night.

Step 2: Determine what you want to get in the end (figure out what the end units should be):

You need to find out how much the oil costs per night so the units we are looking for are US dollars.

Step 3: Determine what conversion factor(s) to use:

$9 = 1 gal

3 oz = 1 night

1 gal = 128 oz

Step 4: Multiply by 1 in the form of the conversion factor that cancels out the unwanted units.

You are starting with 3 ounces per night. To find the cost, multiply \(\dfrac{3\:\text{oz}}{1\:\text{night}}\) by the conversion factors that will enable you to cancel out ounces and gallons and leave you with dollars:

\(\displaystyle \frac{3\:\text{oz}}{1\:\text{night}}\times\frac{1\:\text{gal}}{128\:\text{oz}}\times\frac{\$9}{1\:\text{gal}}\)

Note that each of the two conversion factors, \(\dfrac{1\:\text{gal}}{128\:\text{oz}}\) and \(\dfrac{\$9}{1\:\text{gal}}\) are theoretically equal to 1. This is because anytime you divide something by itself it equals 1, since the numerator is equivalent to the denominator.

Then cancel out ounces and gallons:

\(\displaystyle \frac{3\:\cancel{{\color{Red} \text{oz}}}}{1\:\text{night}}\times\frac{1\:\cancel{{\color{Blue} \text{gal}}}}{128\:\cancel{{\color{Red} \text{oz}}}}\times\frac{\$9}{1\:\cancel{{\color{Blue} \text{gal}}}}\)

Using the zig-zag method you make the calculations in a zig-zag pattern. Remember: Any time you move to the denominator you divide. And any time you move to the numerator, you multiply the following:

The three fractions being multiplied together with arrows indicating the zig-zag method as written below. Arrow from numerator of first fraction to denominator of same fraction, then an arrow from denominator of first fraction to numerator of second fraction, and so on. 

3 ÷ 1 night × 1 ÷ 128 × $9 ÷ 1 = \(\dfrac{$0.2109}{1\:\text{night}}\)

So it will cost about $0.21 per night.
)
4. A truck has a fuel efficiency of 9 milliliters per 100 meters. Find the truck’s fuel efficiency in liters per kilometers using the following information.
1 L = 1000 ml
1 km = 1000 m
(
Solution
x
Solution:
\(\displaystyle \frac{9\:\text{ml}}{100\:\text{m}}\times\frac{1\:\text{L}}{1000\:\text{ml}}\times\frac{1000\:\text{m}}{1\:\text{km}} = \frac{.09\:\text{L}}{1\:\text{km}} \)

(Fuel efficiency is often written as liters per 100 kilometers. If you want to see it this way, you can multiply the numerator and denominator by 100.)

\(\displaystyle \frac{.09\:\text{L}}{1\:\text {km}}\times\frac{100}{100} = \frac {9\:\text{L}}{100\:\text{km}}\)
)
5. How much does it cost to drive 45 kilometers using a car that takes 5 liters of petrol (or gasoline) to go 100 kilometers? The current cost of petrol is €1.50. Round to the nearest hundredth.
5 L = 100 km
€1.50 = 1 L
(
Solution
x
Solution:
\(\displaystyle \frac{45\: {\text{km}}}{1}\times\frac{5\: {\text{L}}}{100\:{\text{km}}}\times\frac{1.50}{1\: {\text{L}}} = 3.38\)
)

    Need More Help?


    1. Study other Math Lessons in the Resource Center.
    2. Visit the Online Tutoring Resources in the Resource Center.
    3. Contact your Instructor.
    4. If you still need help, Schedule a Tutor.