Converting Between Systems
Converting between the U.S. customary system and the metric system requires using unit conversion factors — ratios equal to 1 that change the unit without changing the quantity. Common benchmarks include: 1 inch = 2.54 cm, 1 mile ≈ 1.609 km, 1 pound ≈ 0.454 kg, and 1 gallon ≈ 3.785 liters. Chapter 1 of OpenStax Elementary Algebra 2E covers this skill within the foundations of measurement. Dimensional analysis — multiplying by the correct conversion fraction — is the method that scales to any unit and eliminates guesswork about whether to multiply or divide.
Key Concepts
Property 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.
Common Questions
How do I convert between U.S. and metric units?
Use a conversion factor — a fraction equal to 1 where the numerator and denominator are the same quantity in different units. Multiply your measurement by the conversion factor so the unwanted unit cancels and the desired unit remains.
What are the key conversion facts between U.S. and metric systems?
Key conversions: 1 inch = 2.54 centimeters, 1 mile ≈ 1.609 kilometers, 1 pound ≈ 0.454 kilograms, 1 ounce ≈ 28.35 grams, 1 gallon ≈ 3.785 liters, 1 foot = 0.3048 meters.
What is dimensional analysis?
Dimensional analysis is the process of multiplying a quantity by one or more conversion factors, arranged so that unwanted units cancel. It works for any type of unit conversion and confirms you are multiplying or dividing correctly.
When do students learn unit conversion in algebra?
Unit conversions are covered as part of measurement foundations in algebra 1, appearing in Chapter 1 of OpenStax Elementary Algebra 2E.
How do I know whether to multiply or divide when converting units?
Set up the conversion so the unit you want to eliminate is in the denominator of the conversion fraction. This guarantees it cancels and you end up with the correct unit.
What is a common mistake when converting between systems?
Using the conversion factor upside down, which multiplies instead of divides (or vice versa). Always check that your final answer has the correct unit.
Which textbook covers converting between measurement systems?
OpenStax Elementary Algebra 2E covers this in Chapter 1: Foundations, including both U.S. system and metric system conversion facts.