CHAPTER 2: MEASUREMENT

2-3: U.S. Customary System: Weight

Weight

The oldest, known relic of a weighing scale dates back to around 2000 BCE in the Indus Valley near present day Pakistan. A balance scale uses a counterbalance and works by putting two measurement ends across a fulcrum, placing the object to be measured on one end, and then attaching weight-setting stones on the other. The weight of the object would be then measured according to those stones or weights.[1] Such scales remained the primary method of weight until the Industrial Revolution, and it wasn’t until around 1770 when Richard Salter, a British balance maker, came up with a new type of scale, the spring scale. These mechanical devices, which measure the pressure exerted on a spring to deduce the weight of an object, are still common today since they are cheap, reliable and relatively accurate. As more and more scientific research depended on accurate measurements, scales continued to evolve and led to the creation of the digital scale, first patented in 1980 by Richard Loshbough and Edward Pryor. Digital scales use electrical resistance to detect variations of conductivity according to the pressure put on the material, then deduce the weight of the object on the scale.[2]

Explore Icon Measuring Weight

Weight is a measure of how heavy an item is. In the US Customary System of Measurement weight is measured in ounces, pounds, and tons. The weight of an object is usually measured using a scale. The relationship between the sizes of the units may be represented by the unit conversion equations:

Weight Measures

1 ton = 2000 pounds (lb)

1 pound (lb) = 16 ounces (oz)

 

Explore 1 – Appropriate measures

  1. What is an appropriate measure for the weight of a letter?

Solution

Letters are generally pretty light: Ounces

  1. What is an appropriate measure for the weight of an elephant?

Solution

Elephants are huge animals: Tons

  1. What is an appropriate measure for the weight of a bunch of bananas?

Solution

Bananas are generally measured in pounds

  1. What is an appropriate measure for the weight of a person?

Solutions

People’s weights are measured in pounds

 

Explore 2 – Reading a weight measure

What is the weight of the coffee in pounds? In ounces? If Lily buys twelve bags of coffee at a time, what is the total weight of coffee she buys?

Solution

Reading from the packaging, the coffee weight is 1.75 lbs; 28 oz.

Total weight of 12 bags = 12(1.75 lbs) = 21 lbs.

 

Explore 3 – Basic weight unit conversion

A bridge has the weight limit posted as 15 tons. Calculate the weight limit in pounds:Sign showing 15 tons

Solution

Since 1 ton = 2000 lb, 15 tons = 15 · 1 ton = 15 · 2000 lb = 30,000 lb.

 

Explore 4 – Basic weight unit conversion

A small bakery uses about 6 ounces of cinnamon per day. How many days will 5 pounds of cinnamon supply the bakery? 

Solution

Since there are 16 ounces in a pound, 5 pounds = 5 · 16 ounces = 80 ounces. To determine the number of days, we need to determine how many times 6 oz divides into 80 oz: 80 oz. ÷ 6 oz. = 13.3. Notice that the units cancel to 1.

The cinnamon will last 13 days.

 

Examples

  1. Which is heavier? A soccer ball or a baseball?  A soccer ball weighs about 15 oz while a baseball weighs about 5 oz.
  2. The Nile Crocodile can weigh up to 1650 pounds[3]. What is this weight in tons?
  3. An empty Land Rover Defender can weigh as much as 5735 pounds[4]. What is the weight in tons?
  4. An 80-foot tree with a trunk diameter of 16 inches weighs about 1.91 tons[5]. What is the weight in pounds?

 

Show/Hide Answer
  1. Since 15 oz > 5 oz, a soccer ball is heavier.
  2. There are 2000 lb in a ton. We are converting from a smaller unit (lb) to a larger unit (tons) so we need to divide by 2000: 1650 ÷ 2000 = 0.825. The weight is 0.825 tons.
  3. There are 2000 lb in a ton. We are converting from a smaller unit (lb) to a larger unit (tons) so we need to divide by 2000: 5735 ÷ 2000 = 2.8675. The weight is 2.8675 tons.
  4. There are 2000 lb in a ton. We are converting from a larger unit (tons) to a smaller unit (lb) so we need to multiply by 2000: 1.91(2000) = 3820. The weight is 3820 lbs.

 

 

Reflect Icon

 

  • What is the difference between the two units “ounce” and “fluid ounce”?
Show/Hide Answer

The unit ounce refers to weight. The unit fluid ounce refers to the amount of a non-solid substance (often liquid) enclosed in a 3-dimensional space. One fluid ounce of salt and one fluid ounce of water have different weights. One fluid ounce of salt weighs 1.20 oz. One fluid ounce of water weighs 1.04 oz.

 

Practice Exercises – Weight

  1. A dog weighs 416 oz. What is its weight in pounds?
  2. A pack of strawberries that weighed 0.95 lb contained 23 strawberries. Determine the average weight of a strawberry in ounces.
  3. A gallon of water weighs 8.34 pounds. What does a pint of water weigh in ounces?
  4. Great White Sharks generally weigh between 1500 and 4000 pounds[6]. Describe their weight range in tons.
  5. A pint bottle of water weighs 16.7 oz. Determine the weight of a case of 24 bottles in pounds.
  6. A chocolate chip cookie recipe calls for 4 oz of butter. If liz wants to make six times the recipe, how many pounds of butter should she buy?
Show/Hide Answers
  1. 26 lb.
  2. 0.66 oz.
  3. 16.68 oz.
  4. 0.75 to 2 tons
  5. 25.05 lb.
  6. 1.5 lb.

 

In this section, we will take what we have learned and apply the concepts to new situations.

Perspectives – Weight

  1. Pam’s friend in the UK told her that he’d lost 3.5 stones of weight. If 1 stone = 14 lbs, how much weight did Pam’s friend lose?
  2. David and Andrew ordered 15 cases of champagne for their wedding celebration. If each case of wine weighs about 35 lb, what was the total weight of the champagne they ordered?
  3. A 5 gallon bucket holds 2/3 ft3 of coal that weighs about 33.4 lb[7]. Calculate the weight of coal needed to fill a 4′ by 8′ by 5′ coal bunker in tons.
  4. 1 cubic inch of osmium weighs about 13.1 oz. Calculate the weight of 1 cubic foot of osmium.
  5. Calculate the volume of a rectangular room that measures 25 feet wide by 38 feet long by 10 feet high, in cubic yards.
Show/Hide Answers
  1. 49 lb
  2. 525 lb
  3. 4.008 tons
  4. about 9.3 tons
  5. 351.85 yd3

 

 

Skills Icon In this section, we will use what we have learned so far to practice skill problems.

Skill Exercises

  1. Convert 23.1 tons to pounds
  2. Convert 12,840 pounds to tons
  3. Convert 48 pounds to ounces
  4. Convert 300 ounces to pounds
  5. Convert 56,800 ounces to tons
  6. Convert 0.95 tons to ounces
  7. Convert 300 oz to lb
  8. Convert 35,000 lb to t
  9. Convert 0.45 t to lb
  10. Convert 0.65 t to oz
Show/Hide Answers
  1. 46,200 lb
  2. 6.42 t
  3. 768 oz
  4. 18.75 lb
  5. 1.775 t
  6. 30,400 oz
  7. 18.75 lb
  8. 17.5 t
  9. 900 lb
  10. 20,800 oz

 

 

  1. https://en.wikipedia.org/wiki/Stone_(unit) ↵
  2. https://www.precisa.co.uk/the-history-of-the-weighing-scales/ ↵
  3. https://www.nationalgeographic.com/animals/reptiles/facts/nile-crocodile ↵
  4. http://autopadre.com ↵
  5. https://thetimberlandinvestor.com/how-much-does-a-tree-weigh/ ↵
  6. https://www.britannica.com/animal/white-shark ↵
  7. https://coalpail.com/coal-heating-encyclopedia/volume-anthracite-coal-weight ↵

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