The Mass Of A Paperclip Is $80 \times 10^{-4} \, \text{mg}$. If A Box Of Paperclips Has $7.68 \times 10^4$ Paperclips, Determine The Total Mass Of The Paperclips In The Box. Write The Final Answer In Scientific Notation With The

Introduction

In this article, we will delve into the world of mathematics and explore the concept of mass, specifically the mass of a paperclip. We will begin by examining the mass of a single paperclip and then proceed to calculate the total mass of a box of paperclips. This problem is a great example of how mathematical concepts can be applied to real-world scenarios.

The Mass of a Single Paperclip

The mass of a single paperclip is given as $80 \times 10^{-4} , \text{mg}$. This value represents the mass of a single paperclip in milligrams. To better understand this value, let's break it down. The exponent $10^{-4}$ indicates that the mass is measured in milligrams, where $10^{-4}$ is equivalent to $0.0001$.

Calculating the Total Mass of a Box of Paperclips

Now that we have the mass of a single paperclip, we can proceed to calculate the total mass of a box of paperclips. The box contains $7.68 \times 10^4$ paperclips. To find the total mass, we need to multiply the mass of a single paperclip by the number of paperclips in the box.

Multiplying Mass and Number of Paperclips

To multiply the mass of a single paperclip by the number of paperclips in the box, we can use the following formula:

$$\text{Total Mass} = \text{Mass of a Single Paperclip} \times \text{Number of Paperclips}$$

Substituting the given values, we get:

$$\text{Total Mass} = (80 \times 10^{-4} \, \text{mg}) \times (7.68 \times 10^4)$$

Using the rules of exponents, we can simplify this expression:

$$\text{Total Mass} = 80 \times 7.68 \times 10^{-4} \times 10^4$$

$$\text{Total Mass} = 616.64 \times 10^0$$

Since $10^0$ is equivalent to $1$, we can simplify this expression further:

$$\text{Total Mass} = 616.64 \, \text{mg}$$

Converting to Scientific Notation

To express the total mass in scientific notation, we need to rewrite it in the form $a \times 10^b$, where $a$ is a number between $1$ and $10$, and $b$ is an integer.

In this case, we can rewrite the total mass as:

$$\text{Total Mass} = 6.1664 \times 10^2 \, \text{mg}$$

Conclusion

In this article, we explored the concept of mass, specifically the mass of a paperclip. We began by examining the mass of a single paperclip and then proceeded to calculate the total mass of a box of paperclips. By applying mathematical concepts, we were able to determine the total mass of the paperclips in the box. This problem is a great example of how mathematical concepts can be applied to real-world scenarios.

Discussion

This problem is a great example of how mathematical concepts can be applied to real-world scenarios. The mass of a paperclip is a fundamental concept in physics, and understanding it is crucial in various fields such as engineering and materials science. By applying mathematical concepts, we can gain a deeper understanding of the world around us.

References

• [1] "Mass" by Wikipedia. Retrieved February 27, 2024.
• [2] "Scientific Notation" by Math Is Fun. Retrieved February 27, 2024.

Further Reading

• [1] "Physics for Scientists and Engineers" by Paul A. Tipler and Gene Mosca.
• [2] "Mathematics for Engineers and Scientists" by Donald R. Hill.

Introduction

In our previous article, we explored the concept of mass, specifically the mass of a paperclip. We calculated the total mass of a box of paperclips and expressed it in scientific notation. In this article, we will answer some frequently asked questions related to the mass of a paperclip.

Q&A

Q: What is the mass of a single paperclip?

A: The mass of a single paperclip is given as $80 \times 10^{-4} , \text{mg}$.

Q: How many paperclips are in a box?

A: The box contains $7.68 \times 10^4$ paperclips.

Q: What is the total mass of the paperclips in the box?

A: The total mass of the paperclips in the box is $6.1664 \times 10^2 , \text{mg}$.

Q: Why is it important to express the total mass in scientific notation?

A: Expressing the total mass in scientific notation makes it easier to compare and manipulate large numbers. It also helps to avoid errors when performing calculations.

Q: Can I use a calculator to calculate the total mass?

A: Yes, you can use a calculator to calculate the total mass. However, it's always a good idea to understand the underlying math and calculations to ensure accuracy.

Q: What are some real-world applications of calculating the mass of a paperclip?

A: Calculating the mass of a paperclip has many real-world applications, such as:

• Engineering: Understanding the mass of a paperclip is crucial in engineering applications, such as designing mechanical systems and calculating forces.
• Materials Science: The mass of a paperclip is related to its density and composition, which are important factors in materials science.
• Physics: The mass of a paperclip is a fundamental concept in physics, and understanding it is essential in various fields, such as mechanics and thermodynamics.

Q: Can I use this method to calculate the mass of other objects?

A: Yes, you can use this method to calculate the mass of other objects, as long as you have the mass of a single object and the number of objects.

Q: What are some common mistakes to avoid when calculating the mass of a paperclip?

A: Some common mistakes to avoid when calculating the mass of a paperclip include:

• Rounding errors: Be careful when rounding numbers to avoid errors.
• Incorrect units: Make sure to use the correct units, such as milligrams or grams.
• Incorrect calculations: Double-check your calculations to ensure accuracy.

Conclusion

In this article, we answered some frequently asked questions related to the mass of a paperclip. We hope this Q&A guide has been helpful in understanding the concept of mass and its applications. If you have any further questions, feel free to ask!

Discussion

Calculating the mass of a paperclip is a simple yet important concept in mathematics and physics. Understanding the mass of a paperclip has many real-world applications, and it's essential to be accurate when performing calculations. By following the steps outlined in this article, you can calculate the mass of a paperclip and apply this concept to other objects.

References

• [1] "Mass" by Wikipedia. Retrieved February 27, 2024.
• [2] "Scientific Notation" by Math Is Fun. Retrieved February 27, 2024.

Further Reading

• [1] "Physics for Scientists and Engineers" by Paul A. Tipler and Gene Mosca.
• [2] "Mathematics for Engineers and Scientists" by Donald R. Hill.

Note: The references and further reading section are for additional information and are not directly related to the problem at hand.