Changing Units in the Customary System of Measurement

Instructor: Emily Cadic

Emily has a master's degree in engineering and currently teaches middle and high school science.

Explore customary units and how they can be converted using simple ratios. You will learn the steps for performing a unit conversion calculation with a series of examples and practice problems.

Introduction to Customary Units

Customary units are the standard measurements of length, weight, volume, and time used in the United States. You most likely see numerous examples of customary units throughout any given day. Our clocks and calendars provide us with many different units of time, from seconds to years. We step on a scale to find out our weight in pounds (for better or worse). You can't get through a recipe for homemade cookies without using up all of the measuring cups in your kitchen to get the right volume of each ingredient. And what would football be without the most American of all length measurements, the yard?

The Concept of Unit Conversion

Great; you already have a natural understanding of customary units. Now we will take that one step further as we learn how to convert, or switch, from one unit to another.

Let's start with the football field. Imagine a 10-yard segment of the field, or look at the picture below where each yard has been marked with a red line. Say you have been asked to determine how many feet are in this 10-yard segment. Recall from grade school that there are 3 feet in a yard. Therefore, every time you move 1 yard (or one red segment) you're also moving 3 feet. You should report the length as 30 feet.

10-yard segment of a football field
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Another way to look at this problem is multiplication of ratios. We know that feet and yards have a 3:1 ratio, which can be written one of two ways:

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We have a name for this kind of ratio; it's called a conversion factor and it's the ticket to solving unit conversion problems with greater efficiency. Let's wrap up this football field example with a demonstration of how to apply the correct conversion factor.

Question: How many feet are present in 10 yards?

Solution:

  • What units are you starting with? yards
  • What units do you need to find? feet
  • Which conversion factor should you use? #2 because it contains feet in the numerator

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The key to solving this problem was multiplying by the correct ratio, which brings us to the golden rule of unit conversions: pick the conversion factor that contains the units you would like to find in the numerator, the top number in the ratio.

Customary Units Look-Up Table

For the remainder of this lesson, you can consult the table below for relationships between the different quantities you will encounter when working with customary units.

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Example: Single-Step Unit Conversion

Let's work one more similar problem before we move on to a two-step unit conversion.

Question: How many quarts are present in 4 gallons?

Solution:

  • What units are you starting with? gallons
  • What units do you need to find? quarts
  • What is the relationship between quarts and gallons? 4 quarts in 1 gallon

Remember, your should use a conversion factor that contains 4 quarts in the numerator and 1 gallon in the denominator

Gallons to quarts conversion
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Multi-Step Unit Conversion

Finally, we will go over how to solve a multi-step unit conversion problem. The only difference is we are now going to multiply by more than one conversion factor. You will often be asked to do this sort of calculation when you are working with time. Let's see it in action now!

Question: How many hours are there in one week?

Solution:

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