What Is The Quotient Of $1.06 \times 10^7$ And $2.65 \times 10^4$ Expressed In Scientific Notation?Answer: □ × 10 □ \square \times 10^{\square} □ × 1 0 □

Introduction

Scientific notation is a way of expressing very large or very small numbers in a more manageable form. It involves expressing a number as a product of a number between 1 and 10 and a power of 10. In this article, we will explore the concept of scientific notation and how to find the quotient of two numbers expressed in scientific notation.

Understanding Scientific Notation

Scientific notation is a way of expressing numbers in the form $a \times 10^b$, where $a$ is a number between 1 and 10, and $b$ is an integer. For example, the number 456,789 can be expressed in scientific notation as $4.56789 \times 10^5$.

Dividing Numbers in Scientific Notation

To divide two numbers expressed in scientific notation, we need to follow a specific procedure. The procedure involves dividing the coefficients (the numbers in front of the powers of 10) and subtracting the exponents of the powers of 10.

Step 1: Divide the Coefficients

The first step in dividing two numbers expressed in scientific notation is to divide the coefficients. In this case, we need to divide 1.06 by 2.65.

Step 2: Subtract the Exponents

Once we have divided the coefficients, we need to subtract the exponents of the powers of 10. In this case, we need to subtract 7 from 4.

Step 3: Express the Result in Scientific Notation

After dividing the coefficients and subtracting the exponents, we need to express the result in scientific notation. This involves expressing the result as a product of a number between 1 and 10 and a power of 10.

Calculating the Quotient

Now, let's apply the procedure to find the quotient of $1.06 \times 10^7$ and $2.65 \times 10^4$.

Step 1: Divide the Coefficients

To divide the coefficients, we need to divide 1.06 by 2.65.

$$\frac{1.06}{2.65} = 0.4$$

Step 2: Subtract the Exponents

To subtract the exponents, we need to subtract 7 from 4.

$$7 - 4 = 3$$

Step 3: Express the Result in Scientific Notation

Now, we need to express the result in scientific notation. This involves expressing the result as a product of a number between 1 and 10 and a power of 10.

$$0.4 \times 10^3$$

Conclusion

In this article, we have explored the concept of scientific notation and how to find the quotient of two numbers expressed in scientific notation. We have applied the procedure to find the quotient of $1.06 \times 10^7$ and $2.65 \times 10^4$, and have expressed the result in scientific notation.

Final Answer

The quotient of $1.06 \times 10^7$ and $2.65 \times 10^4$ expressed in scientific notation is $\boxed{0.4 \times 10^3}$.

Frequently Asked Questions

• What is scientific notation?
• How do I express a number in scientific notation?
• How do I divide two numbers expressed in scientific notation?
• What is the quotient of $1.06 \times 10^7$ and $2.65 \times 10^4$ expressed in scientific notation?

Answer to Frequently Asked Questions

• What is scientific notation?

  Scientific notation is a way of expressing very large or very small numbers in a more manageable form. It involves expressing a number as a product of a number between 1 and 10 and a power of 10.

• How do I express a number in scientific notation?

  To express a number in scientific notation, you need to express it as a product of a number between 1 and 10 and a power of 10. For example, the number 456,789 can be expressed in scientific notation as $4.56789 \times 10^5$.

• How do I divide two numbers expressed in scientific notation?

  To divide two numbers expressed in scientific notation, you need to follow a specific procedure. The procedure involves dividing the coefficients (the numbers in front of the powers of 10) and subtracting the exponents of the powers of 10.

• What is the quotient of $1.06 \times 10^7$ and $2.65 \times 10^4$ expressed in scientific notation?

  The quotient of $1.06 \times 10^7$ and $2.65 \times 10^4$ expressed in scientific notation is $\boxed{0.4 \times 10^3}$.

References

• [1] "Scientific Notation." Wikipedia, Wikimedia Foundation, 22 Feb. 2023, en.wikipedia.org/wiki/Scientific_notation.
• [2] "Dividing Numbers in Scientific Notation." Math Is Fun, mathisfun.com/scientific-notation/dividing.html.

Related Articles

• [1] "What is Scientific Notation?" Math Is Fun, mathisfun.com/scientific-notation.html.
• [2] "How to Express a Number in Scientific Notation." Mathway, mathway.com/subject/scientific-notation.
• [3] "How to Divide Two Numbers Expressed in Scientific Notation." Mathway, mathway.com/subject/scientific-notation/division.html.
  

Introduction

Scientific notation is a way of expressing very large or very small numbers in a more manageable form. It involves expressing a number as a product of a number between 1 and 10 and a power of 10. In this article, we will answer some frequently asked questions about scientific notation.

Q&A

Q: What is scientific notation?

A: Scientific notation is a way of expressing very large or very small numbers in a more manageable form. It involves expressing a number as a product of a number between 1 and 10 and a power of 10.

Q: How do I express a number in scientific notation?

A: To express a number in scientific notation, you need to express it as a product of a number between 1 and 10 and a power of 10. For example, the number 456,789 can be expressed in scientific notation as $4.56789 \times 10^5$.

Q: How do I convert a number from standard notation to scientific notation?

A: To convert a number from standard notation to scientific notation, you need to move the decimal point to the left or right until you have a number between 1 and 10. Then, you need to multiply the number by 10 raised to the power of the number of places you moved the decimal point.

Q: How do I add or subtract numbers in scientific notation?

A: To add or subtract numbers in scientific notation, you need to follow the same rules as adding or subtracting numbers in standard notation. However, you need to make sure that the exponents of the powers of 10 are the same.

Q: How do I multiply or divide numbers in scientific notation?

A: To multiply or divide numbers in scientific notation, you need to multiply or divide the coefficients (the numbers in front of the powers of 10) and add or subtract the exponents of the powers of 10.

Q: What is the difference between scientific notation and standard notation?

A: The main difference between scientific notation and standard notation is that scientific notation involves expressing a number as a product of a number between 1 and 10 and a power of 10, while standard notation involves expressing a number in its usual form.

Q: When should I use scientific notation?

A: You should use scientific notation when you need to express a very large or very small number in a more manageable form.

Q: How do I convert a number from scientific notation to standard notation?

A: To convert a number from scientific notation to standard notation, you need to multiply the number by 10 raised to the power of the exponent of the power of 10.

Q: What are some examples of numbers that can be expressed in scientific notation?

A: Some examples of numbers that can be expressed in scientific notation include very large numbers such as 456,789,000,000,000,000 and very small numbers such as 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000