1.2: Weight
- Page ID
- 139255
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You often use the word weight to describe how heavy or light an object or person is. Weight is measured in the U.S. customary system using three units: ounces, pounds, and tons. An ounce is the smallest unit for measuring weight, a pound is a larger unit, and a ton is the largest unit. You can use any of the customary measurement units to describe the weight of something, but it makes more sense to use certain units for certain purposes. For example, it makes more sense to describe the weight of a human being in pounds rather than tons. It makes more sense to describe the weight of a car in tons rather than ounces.
The following table shows the unit conversions and conversion factors that are used to make conversions between customary units of weight.
|
Unit Equivalents |
Conversion Factors (heavier to lighter units of measurement) |
Conversion Factors (lighter to heavier units of measurement) |
|---|---|---|
|
1 pound = 16 ounces |
\(\dfrac{16 \text { ounces }}{1 \text { pound }}\) |
\(\dfrac{1 \text { pound }}{16 \text { ounces }}\) |
|
1 ton = 2000 pounds |
\(\dfrac{2,000 \text { pounds }}{1 \text { ton }}\) |
\(\dfrac{1 \text { ton }}{2,000 \text { pounds }}\) |
Use the Factor Label Method to determine the number of ounces in \( 2 \dfrac{1}{4} \) pounds.
Solution
| \( 2 \dfrac{1}{4} \) pounds = _______ ounces | Begin by reasoning about your answer. Since a pound is heavier than an ounce, expect your answer to be a number greater than \( 2 \dfrac{1}{4} \) |
| \(2 \dfrac{1}{4}\) pounds \(\cdot \dfrac{16 \text { ounces }}{1 \text { pound }}\) = _______ ounces | Multiply by the conversion factor that relates ounces and pounds: \dfrac{16 \; ounces}{1\;pound} |
| \(\dfrac{9 \text { pounds }}{4} \cdot \dfrac{16 \text { ounces }}{1 \text { pound }}\) = _______ ounces | Write the mixed number as an improper fraction. The common unit “pound” can be cancelled because it appears in both the numerator and denominator. |
| \(\dfrac{9}{4} \cdot \dfrac{16 \text { ounces }}{1}\) = _______ ounces | Multiply and simplify. |
| \(\dfrac{9 \cdot 16 \text { ounces }}{4 \cdot 1}\) = _______ ounces | |
| \(\dfrac{144 \text { ounces }}{4}\) = _______ ounces | |
| There are 36 ounces in \(2 \dfrac{1}{4}\) pounds. | |
There are times when you need to perform calculations on measurements that are given in different units. To solve these problems, you need to convert one of the measurements to the same unit of measurement as the other measurement. Think about whether the unit you are
converting to is smaller or larger than the unit you are converting from. This will help you be sure that you are making the right computation. You can use the factor label method to make the conversion from one unit to another.
The following examples require converting between units of weight.
A municipal trash facility allows a person to throw away a maximum of 30 pounds of trash per week. Last week, 140 people threw away the maximum allowable trash. How many tons of trash did this equal?
Solution
| \(140 \cdot 30\) pounds \(=4,200\) pounds | Determine the total trash for the week expressed in pounds. If 140 people each throw away 30 pounds, you can find the total by multiplying. |
| 4,200 pounds = __________ tons | Then convert 4,200 pounds to tons. Reason about your answer. Since a ton is heavier than a pound, expect your answer to be a number less than 4,200. |
| \(\dfrac{4,200 \text { pounds }}{1} \cdot \dfrac{1 \text { ton }}{2,000 \text { pounds }}\) = __________ tons | Find the conversion factor appropriate for the situation: \(\dfrac{1 \text { ton }}{2,000 \text { pounds }}\) |
| \(\dfrac{4,200}{1} \cdot \dfrac{1 \text { ton }}{2,000}\) = __________ tons | |
| \(\dfrac{4,200 \cdot 1 \text { ton }}{1 \cdot 2,000}\) = __________ tons | Multiply and simplify. |
| \(\dfrac{4,200 \text { ton }}{2,000}=2 \dfrac{1}{10}\) tons | |
| The total amount of trash generated is \(2 \dfrac{1}{10}\) tons. | |
The post office charges $0.44 to mail something that weighs an ounce or less. The charge for each additional ounce, or fraction of an ounce, of weight is $0.17. At this rate, how much will it cost to mail a package that weighs 2 pounds 3 ounces?
Solution
| 2 pounds 3 ounces = _______ ounces | Since the pricing is for ounces, convert the weight of the package from pounds and ounces into just ounces. |
| \( \dfrac{2 \text { pounds }}{1} \cdot \dfrac{16 \text { ounces }}{\text { pound }} \) = ________ ounces | First use the factor label method to convert 2 pounds to ounces |
| \( \dfrac{2 \text { pounds }}{1} \cdot \dfrac{16 \text { ounces }}{\text { pound }}\) = ________ ounces | 2 pounds = 32 ounces. |
| \( \dfrac{2}{1} \cdot \dfrac{16 \text { ounces }}{1}=32 \text { ounces }\) | |
| 32 ounces + 3 ounces = 35 ounces | Add the additional 3 ounces to find the weight of the package. The package weighs 35 ounces. There are 34 additional ounces, since 35 – 1 = 34. |
| $0.44 + $0.17(34) | Apply the pricing formula. $0.44 for the first ounce and $0.17 for each additional ounce. |
| $0.44 + $5.78 | |
| $0.44 + $5.78 = $6.22 | |
| It will cost $6.22 to mail a package that weighs 2 pounds 3 ounces. | |
a. How many pounds is 72 ounces?
b. The average weight of a northern Bluefin tuna is 1,800 pounds. The average weight of a great white shark is \(2 \dfrac{1}{2}\) tons. On average, how much more does a great white shark weigh, in pounds, than a northern bluefin tuna?
- Answer
-
a. 4.5 pounds b. 3200 pounds