Measurement and Geometry Unit

3.2 Unit Conversions in the English System

The customary (English) system developed from nonstandard units. The inch was the length of three barleycorns placed end to end. The foot was about the length of an adult’s foot, and the yard was the distance from the tip of a person’s nose to the end of either outstretched arm. The yard was used to measure fabric and other “yard goods.”

Once people realized the need for standardized measurements, the foot was defined as the length of a special metal bar. Then the inch, yard, and mile were defined in terms of a foot.

Part III: Conversions Within The Customary System

Customary Lengths

Customary units of length include inches (in), feet (ft), yards (yd), and miles (m).

  1.     3 feet = ______inches

    2. \(3\;ft\;\times\frac{12\;in}{1\;ft}=36 \) inches

  2.    2 miles = _______feet

    3. \(3\;miles\;\times\frac{5280\;ft}{1\;mile}=10,560 \) feet

  3.    5 feet = _______yards

    4. \(5\;ft\;\times\frac{1\;yd}{3\;ft}=1.67 yds\)

  4.    7 yards = _______ feet

    5. \(7\;yds\;\times\frac{3\;ft}{1\;yd}=21 ft\)

  5.    9 inches = _______feet

    6. \(9\;in\;\times\frac{1\;ft}{12\;in}=0.75 feet\)

  6.    500 yards = _______ miles

    7. \(500\;yds\;\times\frac{1\;mile}{1760\;yds}=0.28 \;miles\)

Customary Mass and Weight

Customary units of weight include ounces (oz), pounds (lb), and tons.

  1.    7 pounds = ______ounces

    2. \(7\;lbs\;\times\frac{16\;oz}{1\;lb}=112\; ounces\)

  2.    300 pounds = ______ tons

    3. \(300\;lbs\;\times\frac{1\;ton}{2000\;lbs}=0.15 \;tons\)

  3.    12 ounces = ______ pounds

    4. \(12\;oz\;\times\frac{1\;lb}{16\;oz}=0.75\; pounds\)

  4.    1 pound = ______ ounces

    5. \(1\;lb\;\times\frac{16\;oz}{1\;lb}=16\;oz\)



Customary Capacity

Customary units of capacity include cups (c), pints (pt), quarts (qt), and gallons(gal).

  1.    3 gallons = ______ quarts

    2. \(3\;gal\;\times\frac{4\;qts}{1\;gal}=12\;quarts\)

  2.    5 cups = ______ pints

    3. \(5\;cups\;\times\frac{1\;pt}{2\;cups}=2.5\;pints\)

  3.    7 pints = ______ quarts

    4. \(7\;pints\;\times\frac{1\;qt}{2\;pt}=3.5\;quarts\)

  4.    12 cups = ______ gallons

    5. \(\underset{}{12\;cups}\;\times\frac{1\;pt}{2\;cups}\times\frac{1\;qt}{2\;pts}\times\frac{1\;gal}{4\;qts}=0.75\;gals\)

Temperature

The German scientist Gabriel Fahrenheit made the first mercury thermometer in 1714. On his scale, he defined 0˚as the temperature of a mixture of equal parts of salt and ice. On this basis, Fahrenheit assigned 32˚ to the freezing point of water, 96˚ to normal body temperature, and 212˚ to the boiling point of water. After his death, an error was discovered in his measurements, and normal body temperature was changed to 98.6˚.

In 1742 Anders Celsius, a Swedish astronomer developed the Celsius (or centigrade) system, in which the boiling point of water was 0˚ and the freezing point was 100˚. Later, the freezing point and boiling point were interchanged.

\(\begin{equation} F=\frac{9}{5} C+32 \end{equation} \)

  1. A temperature of -10°C is about _______ °F.

    2. \(\begin{equation} F=\frac{9}{5}(-10)+32 \end{equation} \)

    \(\begin{equation} F=14° \end{equation} \)

  2. The weather outside is sunny and 15°C. Which of the following would you wear?

    3. a) A heavy coat

    b) A light sweater

    c) A swimsuit

    b) a light sweater

  3. It is a cold day. Which would be a greater increase, an increase of 10°F or an increase of 10°C? Why?

    4. Celsius

  4. Someone who tells you that the temperature is 80° outside

    5. a) is using Fahrenheit

    b) is using Celsius

    c) could be using either Fahrenheit or Celsius

    a) is using Fahrenheit