# 13 The US Measurement System

You may use a calculator throughout this module if needed.

The U.S. customary system of measurement developed from the system used in England centuries ago.^{[1]} To convert from one unit to another, we often have to perform messy calculations like dividing by or multiplying by .

We could solve these unit conversions using proportions, but there is another method that is more versatile, especially when a conversion requires more than one step. This method goes by various names, such as *dimensional analysis* or the *factor label method*. The basic idea is to begin with the measurement you know, then multiply it by a conversion ratio that will cancel the units you don’t want and replace it with the units you do want.

It’s okay if you don’t have the conversion ratios memorized; just be sure to have them available. If you discover other conversion ratios that aren’t provided here, go ahead and write them down!

# U.S. System: Measurements of Length

foot = inches

yard = feet

mile = feet

Let’s walk through two examples to demonstrate the process.

Suppose you’re a fan of Eminem^{[2]} or the Byrds^{[3]} and you’re curious about how many feet are in miles. We can start by writing as a fraction over 1 and then use the conversion ratio to cancel the units.

Now suppose that you want to convert a measurement from feet to miles. (Maybe you’re watching *The Twilight Zone* episode “Nightmare at 20,000 Feet”^{[4]} and wondering how many miles high that is.) We’ll start by writing as a fraction over 1 and then use the conversion ratio to cancel the units.

As it happens, the first situation became a multiplication problem but the second situation became a division problem. Rather than trying to memorize rules about when you’ll multiply versus when you’ll divide, just set up the conversion ratio so the units will cancel out and then the locations of the numbers will tell you whether you need to multiply or divide them.

Exercises

- How many inches are in feet?
- How many feet make up yards?
- yard is equal to how many inches?
- mile is equivalent to how many yards?
- How many feet is inches?
- feet is what length in yards?
- Convert feet into miles.
- How many yards are the same as inches?

Notice that Exercises 3 & 4 give us two more conversion ratios that we could add to our list.

# U.S. System: Measurements of Weight or Mass

pound = ounces

ton = pounds

The procedure is the same; start with the measurement you know and write it as a fraction over 1. Then write the conversion factor so that the units you don’t want will cancel out.

Exercises

- How many ounces are in pounds?
- How many pounds are equivalent to tons?
- Convert ounces to pounds.
- ton is equivalent to what number of ounces?

# U.S. System: Measurements of Volume or Capacity

cup = fluid ounces

pint = cups

quart = pints

gallon = quarts

There are plenty of other conversions that could be provided, such as the number of fluid ounces in a gallon, but let’s keep the list relatively short.

Exercises

- How many fluid ounces are in cups?
- How many pints are in quarts?
- gallon is equal to how many pints?
- How many cups equal quarts?
- Convert cups into gallons.
- How many fluid ounces are in one half gallon?

# U.S. System: Using Mixed Units of Measurement

Measurements are frequently given with mixed units, such as a person’s height being given as ft in instead of in, or a newborn baby’s weight being given as lb oz instead of oz. This can sometimes make the calculations more complicated, but if you can convert between improper fractions and mixed numbers, you can handle this.

Exercises

- A bag of apples weighs ounces. What is its weight in pounds and ounces?
- A carton of orange juice contains fluid ounces. Determine its volume in cups and fluid ounces.
- A hallway is inches long. Give its length in feet and inches.
- The maximum loaded weight of a Ford F-150 pickup truck is lb. Convert this weight into tons and pounds.

We’ll finish up this module by adding and subtracting with mixed units. Again, it may help to think of them as mixed numbers, with a whole number part and a fractional part.

Exercises

Comet weighs lb oz and Fred weighs lb oz.

- Comet and Fred are being put into a cat carrier together. What is their combined weight?
- How much heavier is Fred than Comet?

Two tables are ft in long and ft in long.

- If the two tables are placed end to end, what is their combined length?
- What is the difference in length between the two tables?