The Product Of $1.3 \times 10^{-4}$ And A Number $n$ Results In $2.6 \times 10^{12}$. What Is The Value Of \$n$[/tex\]?A. $2 \times 10^{-8}$ B. $2 \times 10^{-3}$ C. $2 \times

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Introduction

In mathematics, multiplication is a fundamental operation that allows us to find the product of two or more numbers. When we multiply two numbers, we are essentially adding a number a certain number of times, equal to the value of the other number. In this article, we will explore a mathematical problem that involves finding the product of two numbers, and we will use this problem to illustrate the concept of multiplication.

The Problem

The problem states that the product of $1.3 \times 10^{-4}$ and a number $n$ results in $2.6 \times 10^{12}$. We are asked to find the value of $n$. To solve this problem, we need to use the concept of multiplication and the rules of exponents.

Understanding the Concept of Multiplication

Multiplication is a mathematical operation that involves finding the product of two or more numbers. When we multiply two numbers, we are essentially adding a number a certain number of times, equal to the value of the other number. For example, if we multiply 3 by 4, we are adding 3 together 4 times, which gives us a total of 12.

Using the Rules of Exponents

In this problem, we are dealing with numbers that are expressed in scientific notation. Scientific notation is a way of expressing very large or very small numbers in a more manageable form. When we multiply numbers in scientific notation, we need to follow the rules of exponents. The rules of exponents state that when we multiply two numbers with the same base, we add their exponents. For example, if we multiply $2 \times 10^3$ by $3 \times 10^4$, we get $6 \times 10^7$.

Solving the Problem

Now that we have a good understanding of the concept of multiplication and the rules of exponents, we can solve the problem. We are given that the product of $1.3 \times 10^{-4}$ and a number $n$ results in $2.6 \times 10^{12}$. We can set up an equation to represent this relationship:

1.3×10−4×n=2.6×10121.3 \times 10^{-4} \times n = 2.6 \times 10^{12}

To solve for $n$, we can divide both sides of the equation by $1.3 \times 10^{-4}$:

n=2.6×10121.3×10−4n = \frac{2.6 \times 10^{12}}{1.3 \times 10^{-4}}

Using the Rules of Exponents to Simplify the Expression

Now that we have the expression $n = \frac{2.6 \times 10^{12}}{1.3 \times 10^{-4}}$, we can simplify it using the rules of exponents. We can divide the numerator and denominator by $10^{-4}$, which gives us:

n=2.6×10161.3n = \frac{2.6 \times 10^{16}}{1.3}

Evaluating the Expression

Now that we have the expression $n = \frac{2.6 \times 10^{16}}{1.3}$, we can evaluate it to find the value of $n$. We can divide 2.6 by 1.3, which gives us 2. We can then multiply 2 by $10^{16}$, which gives us $2 \times 10^{16}$.

Conclusion

In this article, we have explored a mathematical problem that involves finding the product of two numbers. We have used the concept of multiplication and the rules of exponents to solve the problem. We have found that the value of $n$ is $2 \times 10^{16}$. This problem illustrates the importance of understanding the concept of multiplication and the rules of exponents in mathematics.

Final Answer

The final answer is: 2×1016\boxed{2 \times 10^{16}}

Introduction

In our previous article, we explored a mathematical problem that involved finding the product of two numbers. We used the concept of multiplication and the rules of exponents to solve the problem and found that the value of $n$ is $2 \times 10^{16}$. In this article, we will answer some common questions related to this problem and provide additional insights and explanations.

Q&A

Q: What is the concept of multiplication in mathematics?

A: Multiplication is a mathematical operation that involves finding the product of two or more numbers. When we multiply two numbers, we are essentially adding a number a certain number of times, equal to the value of the other number.

Q: What are the rules of exponents?

A: The rules of exponents state that when we multiply two numbers with the same base, we add their exponents. For example, if we multiply $2 \times 10^3$ by $3 \times 10^4$, we get $6 \times 10^7$.

Q: How do we solve a problem that involves finding the product of two numbers in scientific notation?

A: To solve a problem that involves finding the product of two numbers in scientific notation, we need to follow the rules of exponents. We can multiply the numbers and then simplify the expression using the rules of exponents.

Q: What is the value of $n$ in the problem?

A: The value of $n$ is $2 \times 10^{16}$.

Q: How do we evaluate an expression that involves a product of two numbers in scientific notation?

A: To evaluate an expression that involves a product of two numbers in scientific notation, we need to follow the rules of exponents. We can multiply the numbers and then simplify the expression using the rules of exponents.

Q: What is the importance of understanding the concept of multiplication and the rules of exponents in mathematics?

A: Understanding the concept of multiplication and the rules of exponents is important in mathematics because it allows us to solve problems that involve finding the product of two or more numbers. It is also essential in many real-world applications, such as finance, science, and engineering.

Additional Insights and Explanations

Understanding the Concept of Multiplication

Multiplication is a fundamental operation in mathematics that involves finding the product of two or more numbers. When we multiply two numbers, we are essentially adding a number a certain number of times, equal to the value of the other number. For example, if we multiply 3 by 4, we are adding 3 together 4 times, which gives us a total of 12.

The Rules of Exponents

The rules of exponents state that when we multiply two numbers with the same base, we add their exponents. For example, if we multiply $2 \times 10^3$ by $3 \times 10^4$, we get $6 \times 10^7$. This rule is essential in solving problems that involve finding the product of two numbers in scientific notation.

Solving Problems in Scientific Notation

To solve a problem that involves finding the product of two numbers in scientific notation, we need to follow the rules of exponents. We can multiply the numbers and then simplify the expression using the rules of exponents. For example, if we multiply $2 \times 10^3$ by $3 \times 10^4$, we get $6 \times 10^7$.

Conclusion

In this article, we have answered some common questions related to the problem of finding the product of two numbers. We have provided additional insights and explanations on the concept of multiplication, the rules of exponents, and solving problems in scientific notation. We hope that this article has been helpful in understanding the concept of multiplication and the rules of exponents in mathematics.

Final Answer

The final answer is: 2×1016\boxed{2 \times 10^{16}}