Section 1.2: Weight
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 Factor (heavier to lighter) |
Conversion Factor (lighter to heavier) |
| 1) 1 pound = 16 ounces | [latex]\frac{1~pound}{16~ounces}[/latex] | [latex]\frac{16~ounces}{1~pound}[/latex] |
| 2) 1 ton = 2000 pounds | [latex]\frac{1~ton}{2000~pounds}[/latex] | [latex]\frac{2000~pounds}{1~ton}[/latex] |
Example 4
A Use the Factor Label Method to determine the number of ounces in [latex]2\frac{1}{4}[/latex] pounds.
Solution: State your givens and your goal.
Given: [latex]2\frac{1}{4}[/latex] pounds
Goal: Determine the equivalent number of ounces
1) Begin by reasoning about your answer. Since a pound is heavier than an ounce, expect your answer to be a number greater than [latex]2\frac{1}{4}[/latex].
[latex]2\frac{1}{4}[/latex] pounds = _______ ounces
2) Multiply by the conversion factor that relates ounces and pounds: [latex]\frac{16~ounces}{1~pound}[/latex]
[latex]2\frac{1}{4}[/latex] pounds x [latex]\frac{16~ounces}{1~pound}[/latex] = _____ ounces
3) Write the mixed number as an improper fraction. The common unit “pound” can be cancelled because it appears in both the numerator and denominator.
[latex]\frac{9~\bcancel{pounds}}{4}[/latex] x [latex]\frac{16~ounces}{1~\bcancel{pound}}[/latex] = _____ ounces
4) Multiply and simplify.
[latex]\frac{9}{4}[/latex] x [latex]\frac{16~ounces}{1}[/latex] = [latex]\frac{9~x~16~ounces}{4~x~1}[/latex] = [latex]\frac{144~ounces}{4}[/latex] = 36 ounces
Answer: There are 36 ounces in [latex]2\frac{1}{4}[/latex] 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.
Example 5
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: State your givens and your goal.
Given: maximum of 30 pounds of trash per week per person, 140 people threw away the maximum allowable trash.
Goal: How many tons of trash did this equal?
1) 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.
140 × 30 pounds = 4,200 pounds
2) 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.
4,200 pounds = _____ tons
3) Find the conversion factor appropriate for the situation: [latex]\frac{1~ton}{2000~pounds}[/latex]
[latex]\frac{4200~\bcancel{pounds}}{1}[/latex] x [latex]\frac{1~ton}{2000~\bcancel{pounds}}[/latex] = _____ tons
4) Multiply and simplify. Rewrite your result as a mixed number.
[latex]\frac{4200}{1}[/latex] x [latex]\frac{1~ton}{2000}[/latex] = [latex]\frac{4200~x~1~ton}{1~x~2000}[/latex] = [latex]\frac{4200}{2000}[/latex] tons = [latex]2\frac{1}{10}[/latex] tons
Answer: The total amount of trash generated is [latex]2\frac{1}{10}[/latex] tons.
Example 6
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: State your givens and your goal.
Given: $0.44 to mail something that weighs an ounce or less, each additional ounce of weight is $0.17
Goal: How much will it cost to mail a package that weighs 2 pounds 3 ounces?
1) Since the pricing is for ounces, convert the weight of the package from pounds and ounces into just ounces.
2 pounds 3 ounces = _____ ounces
2) First use the factor label method to convert 2 pounds to ounces.
[latex]\frac{2~\bcancel{pounds}}{1}[/latex] x [latex]\frac{16~oz}{1~\bcancel{pound}}[/latex] = [latex]\frac{2~x~16}{1}[/latex] oz = 32 oz
3) Add the additional 3 ounces to find the weight of the package.
2 pounds 3 ounces = 32 ounces + 3 ounces = 35 ounces
4) Apply the pricing formula. $0.44 for the first ounce and $0.17 for each additional ounce.
$0.44(1) + $0.17(34) = $0.44 + $5.78 = $6.22
Answer: It will cost $6.22 to mail a package that weighs 2 pounds 3 ounces.
Section 1.2 You Try Problems:
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 [latex]2\frac{1}{2}[/latex] tons. On average, how much more does a great white shark weigh, in pounds, than a northern Bluefin tuna?
1.2 – Answers to You Try Problems
a) 4.5 pounds
b) 3200 pounds