Work Out ( 5.2 × 10 15 ) ÷ 10 9 \left(5.2 \times 10^{15}\right) \div 10^9 ( 5.2 × 1 0 15 ) ÷ 1 0 9 .Give Your Answer In Standard Form.

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Introduction

When working with numbers in standard form, we often need to perform various mathematical operations such as addition, subtraction, multiplication, and division. In this article, we will focus on the division operation and learn how to work out (5.2×1015)÷109\left(5.2 \times 10^{15}\right) \div 10^9. We will also provide a step-by-step guide on how to perform this operation and give the answer in standard form.

Understanding Standard Form

Before we dive into the division operation, let's quickly review what standard form is. Standard form is a way of writing very large or very small numbers in a more manageable and concise form. It consists of a number between 1 and 10, multiplied by a power of 10. For example, the number 456,789,012 can be written in standard form as 4.56789012×10114.56789012 \times 10^{11}.

Division Operation

Now that we have a basic understanding of standard form, let's move on to the division operation. When dividing two numbers in standard form, we need to follow a specific set of rules. The rules are as follows:

  • Divide the numbers in the same way as you would with ordinary numbers.
  • If the power of 10 in the divisor is greater than the power of 10 in the dividend, then the result will be a smaller power of 10.
  • If the power of 10 in the divisor is less than the power of 10 in the dividend, then the result will be a larger power of 10.

Step-by-Step Guide

Now that we have a good understanding of the division operation, let's work out (5.2×1015)÷109\left(5.2 \times 10^{15}\right) \div 10^9 step by step.

Step 1: Divide the Numbers

The first step is to divide the numbers in the same way as you would with ordinary numbers. In this case, we need to divide 5.2 by 1 (since 10910^9 can be written as 109=100×10910^9 = 10^0 \times 10^9).

# Import necessary modules
import math

numerator = 5.2
denominator = 1



result = numerator / denominator

Step 2: Determine the Power of 10

The next step is to determine the power of 10 in the result. Since we divided 101510^{15} by 10910^9, the result will be a smaller power of 10. To determine the power of 10, we need to subtract the power of 10 in the divisor from the power of 10 in the dividend.

# Define variables
power_of_10_dividend = 15
power_of_10_divisor = 9


power_of_10_result = power_of_10_dividend - power_of_10_divisor

Step 3: Write the Result in Standard Form

The final step is to write the result in standard form. We have already determined the power of 10 in the result, so we can now write the result in standard form.

# Define variables
result = 5.2 / 1
power_of_10_result = 6


result_standard_form = f"{result} x 10^{power_of_10_result}"

Conclusion

In this article, we learned how to work out (5.2×1015)÷109\left(5.2 \times 10^{15}\right) \div 10^9 using a step-by-step guide. We also reviewed the rules for dividing numbers in standard form and provided a Python code snippet to perform the division operation. Finally, we wrote the result in standard form and provided a concise and easy-to-understand explanation of the division operation.

Frequently Asked Questions

  • Q: What is standard form? A: Standard form is a way of writing very large or very small numbers in a more manageable and concise form. It consists of a number between 1 and 10, multiplied by a power of 10.
  • Q: How do I perform division in standard form? A: To perform division in standard form, you need to follow a specific set of rules. The rules are as follows:
  • Divide the numbers in the same way as you would with ordinary numbers.
  • If the power of 10 in the divisor is greater than the power of 10 in the dividend, then the result will be a smaller power of 10.
  • If the power of 10 in the divisor is less than the power of 10 in the dividend, then the result will be a larger power of 10.
  • Q: How do I write the result in standard form? A: To write the result in standard form, you need to determine the power of 10 in the result and multiply the result by the power of 10.

Further Reading

If you want to learn more about standard form and division operations, we recommend checking out the following resources:

  • Khan Academy: Standard Form
  • Math Is Fun: Standard Form
  • Wolfram Alpha: Division in Standard Form

References

Introduction

In our previous article, we discussed how to work out (5.2×1015)÷109\left(5.2 \times 10^{15}\right) \div 10^9 using a step-by-step guide. We also reviewed the rules for dividing numbers in standard form and provided a Python code snippet to perform the division operation. In this article, we will answer some of the most frequently asked questions about standard form and division operations.

Q&A

Q: What is standard form?

A: Standard form is a way of writing very large or very small numbers in a more manageable and concise form. It consists of a number between 1 and 10, multiplied by a power of 10.

Q: How do I convert a number to standard form?

A: To convert a number to standard form, you need to follow these steps:

  1. Determine if the number is very large or very small.
  2. If the number is very large, multiply it by a power of 10 that is greater than 1.
  3. If the number is very small, multiply it by a power of 10 that is less than 1.
  4. Write the result in the form a×10ba \times 10^b, where aa is the number between 1 and 10, and bb is the power of 10.

Q: How do I perform division in standard form?

A: To perform division in standard form, you need to follow these steps:

  1. Divide the numbers in the same way as you would with ordinary numbers.
  2. If the power of 10 in the divisor is greater than the power of 10 in the dividend, then the result will be a smaller power of 10.
  3. If the power of 10 in the divisor is less than the power of 10 in the dividend, then the result will be a larger power of 10.

Q: How do I write the result in standard form?

A: To write the result in standard form, you need to determine the power of 10 in the result and multiply the result by the power of 10.

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

A: Standard form and scientific notation are two different ways of writing very large or very small numbers. Standard form consists of a number between 1 and 10, multiplied by a power of 10, while scientific notation consists of a number between 1 and 10, multiplied by a power of 10, with the power of 10 written as an exponent.

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

A: To convert a number from scientific notation to standard form, you need to follow these steps:

  1. Write the number in the form a×10ba \times 10^b, where aa is the number between 1 and 10, and bb is the power of 10.
  2. Multiply the number by the power of 10, and write the result in the form a×10ba \times 10^b.

Q: What are some common mistakes to avoid when working with standard form and division operations?

A: Some common mistakes to avoid when working with standard form and division operations include:

  • Not following the rules for dividing numbers in standard form.
  • Not writing the result in standard form.
  • Not using the correct power of 10.
  • Not converting numbers from scientific notation to standard form correctly.

Conclusion

In this article, we answered some of the most frequently asked questions about standard form and division operations. We hope that this article has been helpful in clarifying any confusion you may have had about these topics. If you have any further questions, please don't hesitate to ask.

Further Reading

If you want to learn more about standard form and division operations, we recommend checking out the following resources:

  • Khan Academy: Standard Form
  • Math Is Fun: Standard Form
  • Wolfram Alpha: Division in Standard Form

References