Module 13: The US Measurement System

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19 Module 13: The US Measurement System — Technical Mathematics

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Robin the orange cat under a US bicentennial flag

Robin the cat has the spirit of ’76.

You may use a calculator throughout this module.

This system used to be called the English system, but now the U.S. has the dubious honor of being associated with the system that uses inches, feet, miles, ounces, pounds, cups, gallons, etc. To convert from one unit to another, we often have to perform messy calculations like dividing by $16$ or multiplying by $5,280$ .

We could solve these unit conversions using proportions, but there is another method than 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

$1$ foot = $12$ inches

$1$ yard = $3$ feet

$1$ mile = $5,280$ feet

Exercises

1. How many inches are in $4.5$ feet?

2. How many feet make up $18$ yards?

3. $1$ yard is equal to how many inches?

4. $1$ mile is equivalent to how many yards?

5. How many feet is $176$ inches?

6. $45$ feet is what length in yards?

7. Convert $10,560$ feet into miles.

8. How many yards are the same as $1,080$ 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

$1$ pound = $16$ ounces

$1$ ton = $2,000$ pounds

Exercises

9. How many ounces are in $2.5$ pounds?

10. How many pounds are equivalent to $1.2$ tons?

11. Convert $300$ ounces to pounds.

12. $1$ ton is equivalent to what number of ounces?

U.S. System: Measurements of Volume or Capacity

$1$ cup = $8$ fluid ounces

$1$ pint = $2$ cups

$1$ quart = $2$ pints

$1$ gallon = $4$ 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

13. How many fluid ounces are in $6$ cups?

14. How many pints are in $3.5$ quarts?

15. $1$ gallon is equal to how many pints?

16. How many cups equal $1.25$ quarts?

17. Convert $20$ cups into gallons.

18. 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 $5$ ft $7$ in instead of $67$ in, or a newborn baby’s weight being given as $8$ lb $3$ oz instead of $131$ 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

19. A bag of apples weighs $55$ ounces. What is its weight in pounds and ounces?

20. A carton of orange juice contains $59$ fluid ounces. Determine its volume in cups and fluid ounces.

21. A hallway is $182$ inches long. Give its length in feet and inches.

22. The maximum loaded weight of a Ford F-150 pickup truck is $8,500$ 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