Module 2
1. Module 2
1.19. Page 4
Module 2: The Imperial System
Bringing Ideas Together
pound (lb): a unit of weight (mass) in the imperial system
One pound is defined as exactly 0.453 592 37 kg.
In Explore and Get Started you weighed items in pounds. The pound as a unit of weight dates back at least as far as the time of the Romans. As a matter of interest, the symbol for one pound is 1 lb. This symbol is an abbreviation of the Latin word libra—the word for a set of scales used for weighing.
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Did You Know?
The symbol for the birth sign Libra is a set of scales! The constellation Libra is thought to look like a set of scales.
© EdBockStock/shutterstock
Nowadays, a set of scales is considered to be any instrument that measures weight (mass). An instrument that measures weight does not have to be made up of two pans connected to a bar. For example, bathroom scales are often compact devices that have a spring-loaded platform that moves down in response to the weight on it.
A pound is about half a kilogram. Look at the wrapping on a pound of butter. You will recall that Curtis read that the brick of butter was 454 grams. Is 1 lb more or less than one-half kilogram? Because 0.5 kg = 500 g, 1 lb is less than 0.5 kg.
Did You Know?
The Roman pound was divided into 12 parts. The Latin word uncia for “twelfth part,” as you will recall, gave the word inch. It also gives the English word ounce.
The troy pound, used for precious metals, such as gold and silver, still has 12 ounces. However, the modern pound commonly used for weight (mass) is divided into 16 ounces!
ounce (oz): a unit of weight (mass) in the imperial system
There are 16 oz in 1 lb.
1 lb = 16 oz
The following examples deal with the relationship between pounds and ounces.
Example 1
Nutritionists recommend active teenage girls eat 5 oz of protein each day. How many pounds of protein would this recommendation be over a 30-day month?
Solution
Now convert ounces to pounds. Remember 1 lb = 16 oz.
The recommended monthly protein requirement is 9.375 lb.
Example 2
Krysta’s baby was 6 lb 7 oz when she was born. Altogether, how many ounces did the newborn weigh?
View the animated “Example 2 Solution.”
It’s time to weigh your skills.
Self-Check
Respond to the following questions.
SC 1. An average egg weighs about 2 oz. How much would two dozen eggs weigh?
SC 2. A butcher slices a 5-lb ham into 160 pieces. What is the average weight in ounces per slice?
SC 3. Emile’s cat has 7 kittens. Each kitten weighs 3 oz. What is their total weight in pounds and ounces?
SC 4. Victor and his friends caught 30 perch. The total catch weighed 15 lb. On average, how many ounces did each perch weigh?
© Bram van Broekhoven/shutterstock
What unit did you use in the metric system for large masses such as the mass of a load of sand? Large masses were measured in tonnes. 1 t = 1000 kg
In the imperial system, large weights such as the weight of sand being hauled in a truck, is measured in tons. There are short tons and long tons.
ton: a unit of weight (mass) in the imperial system (also called a short ton)
1 ton = 2000 lb
short ton: a unit of weight (mass) in the imperial system (also called a ton)
1 short ton = 2000 lb
long ton: a unit of weight (mass) in the imperial system
1 long ton = 2240 lb
Did You Know?
The British defined the ton as equal to 160 stone when they considered the stone as the basic unit of weight. One stone equals 14 lb. Therefore, the British ton, now also known as the long ton, is equal to 2240 lb.
Since 1 kg is about 2.2 lb, what would an approximation of the metric tonne be in pounds? Do you agree that
1 tonne =
Which is a metric tonne closer to—a short ton or a long ton? Since 1 tonne is almost 2200 lb, 1 metric tonne and 1 long ton are almost the same!
Study these examples to see how to apply the definitions of tons.
Example 3
Mr. Watnee hauls gravel. He estimates that 1 yd3 weighs 3000 lb. How many tons (short) would a 5-yd3 load of gravel weigh?
Solution
So,
Mr. Watnee’s load of gravel weighs 7.5 tons.
Self-Check
Do the following questions.
SC 5. Sergey loaded 200 bushels of wheat into the box of his truck. The grain weighed 5.2 tons (short). How many pounds did each bushel of wheat weigh?
SC 6. If 1 yd3 of gravel weighs 1.5 tons, how many pounds does 1 ft3 of gravel weigh? Round your answer to the nearest pound.
Mass Conversions
As for length, area, volume, and capacity, there is a need, from time-to-time, to convert masses (weights) between the imperial and SI systems. Remember that the pound was defined in terms of the kilogram. One pound is defined as exactly 0.453 592 37 kg.
So, you can set up tables to convert between systems. First work through the following example.
Example 4
How many grams are there in 1 oz?
Solution
So,
There are approximately 28 g in 1 oz.
Self-Check
Now you will complete a set of tables for converting among imperial and SI units.
Do the following questions.
SC 7. Complete the following table by filling in the missing entries. Round to 4 decimal places.
|
Imperial |
Metric |
|
1 oz |
28.3495 g |
|
1 lb |
0.4536 kg |
|
1 ton (short) = 2000 lb |
__________ t |
|
1 ton (long) = 2240 lb |
__________ t |
SC 8. Complete the following table by filling in the missing entries. Round to 4 decimal places.
|
Metric |
Imperial |
|
1 g |
__________ oz |
|
1 kg |
__________ lb |
|
1 t |
__________ ton (short) |
|
1 t |
__________ ton (long) |
Now you can use the tables from SC 7 and SC 8 to convert weights and masses! Study these examples. You may wish to do the questions first and then compare your answers to the given solutions.
Example 5
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Gabi weighs 116 lb. What is her mass to the nearest kilogram?
Solution
So,
Gabi’s mass is about 53 kg (to the nearest kg).
Now check your skills in converting between imperial weights and SI masses.
You may also use the multimedia “Imperial to SI Weight Conversion” to confirm your calculations for the questions that follow.
Self-Check
Do the following questions.
SC 9. Apples cost $0.79 per pound. What is their cost per kilogram? Round your answer to the nearest cent.
SC 10. The mass of a Canadian two-dollar coin is 7.3 g. What is its weight in ounces?
SC 11. How much does 1 gal of water weigh in pounds if 1 L of water has a mass of 1 kg? Round your answer to the nearest pound.
Mastering Concepts
Try this question. You will apply your knowledge from a previous lesson about volume and capacity.
Connie is planning to lay a concrete driveway 60 ft long, 15 ft wide, and 4 in thick. If 1 yd3 of concrete weighs 4000 lb, how many tons of concrete are needed for the driveway? Round your answer to 1 decimal place.