Chapter 1: Problem 23
How much will 1000 washers weigh if each weighs 2.375 g?
Short Answer
Expert verified
2375 grams or 2.375 kilograms
Step by step solution
01
Understand the problem
You need to find the total weight of 1000 washers, each weighing 2.375g. This is a multiplication problem where you multiply the quantity of items by the weight of one item.
02
Set up the calculation
Multiply the number of washers (1000) by the weight of one washer (2.375g) to find the total weight.
03
Perform the multiplication
Calculate 1000 times 2.375 to find the total weight in grams.
04
Converting to a heavier unit (optional)
If a heavier unit like kilograms is desired, divide the result by 1000 to convert grams to kilograms.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Arithmetic Operations
Arithmetic operations are the foundation of mathematics and include addition, subtraction, multiplication, and division. These operations are essential for solving everyday problems and mathematical expressions.
In our textbook exercise, the focus is on multiplication, which is the operation of scaling one number by another. It is used when we need to combine multiple groups of the same size, as is the case with finding the total weight of multiple items like our washers. The formula used is straightforward: if you have 'a' groups of 'b' size, the total size is calculated as \(a \times b\).
For example, if each washer weighs 2.375 grams and we have 1000 of them, we simply multiply these numbers. The calculation \(1000 \times 2.375\) is basic multiplication, and it represents the total weight of the washers in grams. It is critical that the multiplication process is understood because it forms the basis of many mathematical applications.
In our textbook exercise, the focus is on multiplication, which is the operation of scaling one number by another. It is used when we need to combine multiple groups of the same size, as is the case with finding the total weight of multiple items like our washers. The formula used is straightforward: if you have 'a' groups of 'b' size, the total size is calculated as \(a \times b\).
For example, if each washer weighs 2.375 grams and we have 1000 of them, we simply multiply these numbers. The calculation \(1000 \times 2.375\) is basic multiplication, and it represents the total weight of the washers in grams. It is critical that the multiplication process is understood because it forms the basis of many mathematical applications.
Unit Conversion
Unit conversion is a critical concept, especially when working with measurements. Mathematics is not just about calculating numbers; it's also about applying the correct units and making sure that the results make sense in real-world situations. Converting units allows us to express measurements in different scales so they can be understood and used appropriately.
In the context of our original exercise, once we have the total weight of the washers in grams, we might need to convert it to a more suitable unit, such as kilograms, to match the context in which the weight is being considered, such as shipping regulations or material handling guidelines. This is typically done by dividing or multiplying by a conversion factor.
To convert grams to kilograms, since there are 1000 grams in a kilogram, we divide the result by 1000. For instance, if the sum of 1000 washers' weight in grams is 2375g, dividing by 1000 gives us the weight in kilograms: \(2375 \text{ g} ÷ 1000 = 2.375 \text{ kg}\).
In the context of our original exercise, once we have the total weight of the washers in grams, we might need to convert it to a more suitable unit, such as kilograms, to match the context in which the weight is being considered, such as shipping regulations or material handling guidelines. This is typically done by dividing or multiplying by a conversion factor.
To convert grams to kilograms, since there are 1000 grams in a kilogram, we divide the result by 1000. For instance, if the sum of 1000 washers' weight in grams is 2375g, dividing by 1000 gives us the weight in kilograms: \(2375 \text{ g} ÷ 1000 = 2.375 \text{ kg}\).
Practical Math Applications
Mathematics is not just abstract numbers; it serves numerous practical purposes in everyday life. The principles of arithmetic operations and unit conversion come into play in fields such as engineering, construction, cooking, shopping, and science.
For our washers example, we can see practical applications in inventory management and procurement in manufacturing, where knowing the total weight is essential for logistics planning and cost calculations. To answer questions like 'how much space is needed to store the washers?' or 'what will the shipping cost be?,' one must understand not only the concept of multiplication but also be able to convert units and apply the results in a practical way.
For example, understanding the total weight is valuable when calculating shipping costs or determining if the floor can support the weight of the stored material. In these cases, being able to apply mathematical calculations to derive meaningful information for practical scenarios is a fundamental skill. This integration of math into real-life situations showcases its value beyond just solving textbook problems.
For our washers example, we can see practical applications in inventory management and procurement in manufacturing, where knowing the total weight is essential for logistics planning and cost calculations. To answer questions like 'how much space is needed to store the washers?' or 'what will the shipping cost be?,' one must understand not only the concept of multiplication but also be able to convert units and apply the results in a practical way.
For example, understanding the total weight is valuable when calculating shipping costs or determining if the floor can support the weight of the stored material. In these cases, being able to apply mathematical calculations to derive meaningful information for practical scenarios is a fundamental skill. This integration of math into real-life situations showcases its value beyond just solving textbook problems.
