In this lesson from OpenStax Elementary Algebra 2E, students learn how to make unit conversions within the U.S. system and the metric system, use mixed units of measurement, and convert between the two systems as well as between Fahrenheit and Celsius temperatures. The core technique taught is using the identity property of multiplication to set up unit fractions that cancel unwanted units, applied to length, weight, volume, and time. This foundational algebra lesson is suitable for students transitioning from pre-algebra into a first formal algebra course.
Section 1
📘 Systems of Measurement
This lesson introduces the U.S. and metric measurement systems. You'll master converting units for length, weight, volume, and temperature by using conversion factors, a powerful application of the identity property of multiplication.
Next, you'll see this in action through worked examples and then apply your skills with a series of interactive practice cards to master unit conversions.
Section 2
U.S. System of Measurement
The U.S. system of measurement uses units of inch, foot, yard, and mile to measure length and pound and ton to measure weight. For capacity, the units used are cup, pint, quart, and gallons. To convert between units, we use the identity property of multiplication, writing 1 as a fraction that helps convert the units, such as .
Length
1 foot (ft.) = 12 inches (in.)
1 yard (yd.) = 3 feet (ft.)
1 mile (mi.) = 5,280 feet (ft.)
Weight
1 pound (lb.) = 16 ounces (oz.)
1 ton = 2000 pounds (lb.)
Section 3
Metric System of Measurement
In the metric system, units are related by powers of 10. The root words of their names reflect this relation. The basic unit for measuring length is a meter. One kilometer is 1,000 meters; the prefix kilo means thousand. One centimeter is of a meter.
To multiply by 10, 100, or 1,000, we move the decimal to the right one, two, or three places, respectively. To multiply by 0.1, 0.01, or 0.001, we move the decimal to the left one, two, or three places, respectively.
Length
1 kilometer (km) = 1,000 meters (m)
1 meter (m) = 100 centimeters (cm)
1 meter (m) = 1,000 millimeters (mm)
Section 4
Converting Between Systems
To work easily in both the U.S. and metric systems, we need to be able to convert between them. We make conversions between the systems just as we do within the systems—by multiplying by unit conversion factors.
Common Conversion Factors
Length
1 in. = 2.54 cm
1 mi. = 1.61 km
1 m = 3.28 ft.
Section 5
Temperature Conversion
The U.S. and metric systems use different scales to measure temperature. The U.S. system uses degrees Fahrenheit, written °F. The metric system uses degrees Celsius, written °C.
To convert from Fahrenheit temperature, , to Celsius temperature, , use the formula:
To convert from Celsius temperature, , to Fahrenheit temperature, , use the formula:
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Section 1
📘 Systems of Measurement
This lesson introduces the U.S. and metric measurement systems. You'll master converting units for length, weight, volume, and temperature by using conversion factors, a powerful application of the identity property of multiplication.
Next, you'll see this in action through worked examples and then apply your skills with a series of interactive practice cards to master unit conversions.
Section 2
U.S. System of Measurement
The U.S. system of measurement uses units of inch, foot, yard, and mile to measure length and pound and ton to measure weight. For capacity, the units used are cup, pint, quart, and gallons. To convert between units, we use the identity property of multiplication, writing 1 as a fraction that helps convert the units, such as .
Length
1 foot (ft.) = 12 inches (in.)
1 yard (yd.) = 3 feet (ft.)
1 mile (mi.) = 5,280 feet (ft.)
Weight
1 pound (lb.) = 16 ounces (oz.)
1 ton = 2000 pounds (lb.)
Section 3
Metric System of Measurement
In the metric system, units are related by powers of 10. The root words of their names reflect this relation. The basic unit for measuring length is a meter. One kilometer is 1,000 meters; the prefix kilo means thousand. One centimeter is of a meter.
To multiply by 10, 100, or 1,000, we move the decimal to the right one, two, or three places, respectively. To multiply by 0.1, 0.01, or 0.001, we move the decimal to the left one, two, or three places, respectively.
Length
1 kilometer (km) = 1,000 meters (m)
1 meter (m) = 100 centimeters (cm)
1 meter (m) = 1,000 millimeters (mm)
Section 4
Converting Between Systems
To work easily in both the U.S. and metric systems, we need to be able to convert between them. We make conversions between the systems just as we do within the systems—by multiplying by unit conversion factors.
Common Conversion Factors
Length
1 in. = 2.54 cm
1 mi. = 1.61 km
1 m = 3.28 ft.
Section 5
Temperature Conversion
The U.S. and metric systems use different scales to measure temperature. The U.S. system uses degrees Fahrenheit, written °F. The metric system uses degrees Celsius, written °C.
To convert from Fahrenheit temperature, , to Celsius temperature, , use the formula:
To convert from Celsius temperature, , to Fahrenheit temperature, , use the formula:
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter