Work Out \left(4 \times 10^4\right) \times\left(2 \times 10^3\right ]. Give Your Answer In Standard Form.

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Introduction

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When working with large numbers, it's often more convenient to express them in standard form, which is a way of writing numbers as a product of a number between 1 and 10 and a power of 10. In this article, we'll explore how to multiply numbers in standard form and provide a step-by-step guide to solving the given problem.

What is Standard Form?

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Standard form is a way of writing numbers as a product of a number between 1 and 10 and a power of 10. It's commonly used to express large or small numbers in a more manageable form. For example, the number 456,000 can be written in standard form as $4.56 \times 10^5$. This makes it easier to perform calculations and compare numbers.

Multiplying Numbers in Standard Form

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When multiplying numbers in standard form, we need to follow a specific procedure to ensure that we get the correct result. Here are the steps:

1. Multiply the coefficients: Multiply the numbers between 1 and 10 that are being multiplied.
2. Add the exponents: Add the powers of 10 that are being multiplied.
3. Write the result in standard form: Combine the result of the coefficient multiplication with the result of the exponent addition.

Work out $\left(4 \times 10^4\right) \times\left(2 \times 10^3\right)$

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Now, let's apply the steps above to the given problem.

Step 1: Multiply the coefficients

The coefficients are 4 and 2. Multiplying them together gives:

$$4 \times 2 = 8$$

Step 2: Add the exponents

The exponents are $10^4$ and $10^3$. Adding them together gives:

$$10^4 + 10^3 = 10^7$$

Step 3: Write the result in standard form

Combining the result of the coefficient multiplication with the result of the exponent addition gives:

$$8 \times 10^7$$

Conclusion

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In this article, we've explored how to multiply numbers in standard form and provided a step-by-step guide to solving the given problem. By following the procedure outlined above, we can easily multiply numbers in standard form and get the correct result.

Frequently Asked Questions

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Q: What is standard form?

A: Standard form is a way of writing numbers as a product of a number between 1 and 10 and a power of 10.

Q: How do I multiply numbers in standard form?

A: To multiply numbers in standard form, you need to multiply the coefficients and add the exponents.

Q: What is the result of $\left(4 \times 10^4\right) \times\left(2 \times 10^3\right)$?

A: The result is $8 \times 10^7$.

Further Reading

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If you want to learn more about standard form and how to multiply numbers in this form, here are some additional resources:

• Maths Is Fun: Standard Form
• BBC Bitesize: Standard Form
• [Khan Academy: Standard Form](https://www.khanacademy.org/math/algebra/x2f6f7c7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f
  

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Q: What is standard form?

A: Standard form is a way of writing numbers as a product of a number between 1 and 10 and a power of 10. It's commonly used to express large or small numbers in a more manageable form.

Q: How do I multiply numbers in standard form?

A: To multiply numbers in standard form, you need to follow these steps:

1. Multiply the coefficients: Multiply the numbers between 1 and 10 that are being multiplied.
2. Add the exponents: Add the powers of 10 that are being multiplied.
3. Write the result in standard form: Combine the result of the coefficient multiplication with the result of the exponent addition.

Q: What is the result of $\left(4 \times 10^4\right) \times\left(2 \times 10^3\right)$?

A: The result is $8 \times 10^7$.

Q: Can I multiply numbers in standard form by hand?

A: Yes, you can multiply numbers in standard form by hand. However, it's often easier to use a calculator or a computer program to perform the calculation.

Q: How do I divide numbers in standard form?

A: To divide numbers in standard form, you need to follow these steps:

1. Divide the coefficients: Divide the numbers between 1 and 10 that are being divided.
2. Subtract the exponents: Subtract the powers of 10 that are being divided.
3. Write the result in standard form: Combine the result of the coefficient division with the result of the exponent subtraction.

Q: What is the result of $\left(8 \times 10^7\right) \div \left(2 \times 10^3\right)$?

A: The result is $4 \times 10^4$.

Q: Can I add or subtract numbers in standard form?

A: Yes, you can add or subtract numbers in standard form. However, you need to make sure that the numbers have the same exponent.

Q: How do I add or subtract numbers in standard form?

A: To add or subtract numbers in standard form, you need to follow these steps:

1. Add or subtract the coefficients: Add or subtract the numbers between 1 and 10 that are being added or subtracted.
2. Keep the same exponent: Keep the same exponent for both numbers.
3. Write the result in standard form: Combine the result of the coefficient addition or subtraction with the same exponent.

Q: What is the result of $\left(3 \times 10^4\right) + \left(2 \times 10^4\right)$?

A: The result is $5 \times 10^4$.

Q: What is the result of $\left(5 \times 10^4\right) - \left(2 \times 10^4\right)$?

A: The result is $3 \times 10^4$.

Q: Can I convert a number from standard form to decimal form?

A: Yes, you can convert a number from standard form to decimal form by multiplying the coefficient by the power of 10.

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

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

1. Multiply the coefficient: Multiply the coefficient by the power of 10.
2. Write the result in decimal form: Write the result as a decimal number.

Q: What is the result of converting $4 \times 10^5$ to decimal form?

A: The result is $400,000$.

Q: What is the result of converting $3 \times 10^3$ to decimal form?

A: The result is $3,000$.

Q: Can I convert a number from decimal form to standard form?

A: Yes, you can convert a number from decimal form to standard form by expressing the number as a product of a number between 1 and 10 and a power of 10.

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

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

1. Determine the power of 10: Determine the power of 10 that the number can be expressed as.
2. Write the result in standard form: Write the result as a product of a number between 1 and 10 and the power of 10.

Q: What is the result of converting 456,000 to standard form?

A: The result is $4.56 \times 10^5$.

Q: What is the result of converting 3,000 to standard form?

A: The result is $3 \times 10^3$.