Simplify $\left(2.2 \times 10^{11}\right) \div \left(1 \times 10^4\right$\] And Write The Answer In Scientific Notation.A. $2.2 \times 10^{15}$ B. 22 C. $2.2 \times 10^7$ D. $2.2 \times 10^4$

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Understanding Scientific Notation

Scientific notation is a way of expressing very large or very small numbers in a more manageable form. It consists of a number between 1 and 10, multiplied by a power of 10. For example, the number 456,000 can be written in scientific notation as 4.56 × 10^5. This makes it easier to perform calculations and comparisons with large or small numbers.

Dividing Numbers in Scientific Notation

When dividing numbers in scientific notation, we divide the coefficients (the numbers in front of the powers of 10) and subtract the exponents of the powers of 10. This is based on the rule that a^m ÷ a^n = a^(m-n). Let's apply this rule to the given problem.

Simplifying the Expression

We are given the expression $\left(2.2 \times 10^{11}\right) \div \left(1 \times 10^4\right)$. To simplify this expression, we divide the coefficients and subtract the exponents of the powers of 10.

$\left(2.2 \times 10^{11}\right) \div \left(1 \times 10^4\right) = \frac{2.2}{1} \times \frac{10^{11}}{10^4}$

Applying the Rule for Dividing Powers of 10

When dividing powers of 10, we subtract the exponents. In this case, we have 10^11 ÷ 10^4 = 10^(11-4) = 10^7.

$\frac{2.2}{1} \times \frac{10^{11}}{10^4} = 2.2 \times 10^7$

Writing the Answer in Scientific Notation

The simplified expression is 2.2 × 10^7, which is already in scientific notation. Therefore, the answer is $\boxed{2.2 \times 10^7}$.

Conclusion

In this article, we simplified the expression $\left(2.2 \times 10^{11}\right) \div \left(1 \times 10^4\right)$ and wrote the answer in scientific notation. We applied the rule for dividing numbers in scientific notation, which involves dividing the coefficients and subtracting the exponents of the powers of 10. The final answer is $\boxed{2.2 \times 10^7}$.

Frequently Asked Questions

• What is scientific notation?
• How do you divide numbers in scientific notation?
• What is the rule for dividing powers of 10?

Answers 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 consists of a number between 1 and 10, multiplied by a power of 10.
• How do you divide numbers in scientific notation? When dividing numbers in scientific notation, we divide the coefficients (the numbers in front of the powers of 10) and subtract the exponents of the powers of 10.
• What is the rule for dividing powers of 10? When dividing powers of 10, we subtract the exponents. For example, 10^11 ÷ 10^4 = 10^(11-4) = 10^7.
  

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Understanding Scientific Notation

Scientific notation is a way of expressing very large or very small numbers in a more manageable form. It consists of a number between 1 and 10, multiplied by a power of 10. For example, the number 456,000 can be written in scientific notation as 4.56 × 10^5. This makes it easier to perform calculations and comparisons with large or small numbers.

Dividing Numbers in Scientific Notation

When dividing numbers in scientific notation, we divide the coefficients (the numbers in front of the powers of 10) and subtract the exponents of the powers of 10. This is based on the rule that a^m ÷ a^n = a^(m-n). Let's apply this rule to the given problem.

Simplifying the Expression

We are given the expression $\left(2.2 \times 10^{11}\right) \div \left(1 \times 10^4\right)$. To simplify this expression, we divide the coefficients and subtract the exponents of the powers of 10.

$\left(2.2 \times 10^{11}\right) \div \left(1 \times 10^4\right) = \frac{2.2}{1} \times \frac{10^{11}}{10^4}$

Applying the Rule for Dividing Powers of 10

When dividing powers of 10, we subtract the exponents. In this case, we have 10^11 ÷ 10^4 = 10^(11-4) = 10^7.

$\frac{2.2}{1} \times \frac{10^{11}}{10^4} = 2.2 \times 10^7$

Writing the Answer in Scientific Notation

The simplified expression is 2.2 × 10^7, which is already in scientific notation. Therefore, the answer is $\boxed{2.2 \times 10^7}$.

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 consists of a number between 1 and 10, multiplied by a power of 10.

Q: How do you divide numbers in scientific notation?

A: When dividing numbers in scientific notation, we divide the coefficients (the numbers in front of the powers of 10) and subtract the exponents of the powers of 10.

Q: What is the rule for dividing powers of 10?

A: When dividing powers of 10, we subtract the exponents. For example, 10^11 ÷ 10^4 = 10^(11-4) = 10^7.

Q: Can you give an example of a number in scientific notation?

A: Yes, the number 456,000 can be written in scientific notation as 4.56 × 10^5.

Q: How do you simplify an expression with exponents?

A: To simplify an expression with exponents, we apply the rule that a^m ÷ a^n = a^(m-n).

Q: What is the final answer to the given problem?

A: The final answer to the given problem is $\boxed{2.2 \times 10^7}$.

Conclusion

In this article, we simplified the expression $\left(2.2 \times 10^{11}\right) \div \left(1 \times 10^4\right)$ and wrote the answer in scientific notation. We applied the rule for dividing numbers in scientific notation and the rule for dividing powers of 10. The final answer is $\boxed{2.2 \times 10^7}$.

Frequently Asked Questions

• What is scientific notation?
• How do you divide numbers in scientific notation?
• What is the rule for dividing powers of 10?

Answers 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 consists of a number between 1 and 10, multiplied by a power of 10.
• How do you divide numbers in scientific notation? When dividing numbers in scientific notation, we divide the coefficients (the numbers in front of the powers of 10) and subtract the exponents of the powers of 10.
• What is the rule for dividing powers of 10? When dividing powers of 10, we subtract the exponents. For example, 10^11 ÷ 10^4 = 10^(11-4) = 10^7.

Additional Resources

• For more information on scientific notation, visit www.mathisfun.com.
• For more practice problems on dividing numbers in scientific notation, visit www.khanacademy.org.

Conclusion

In conclusion, scientific notation is a powerful tool for expressing very large or very small numbers in a more manageable form. By applying the rule for dividing numbers in scientific notation and the rule for dividing powers of 10, we can simplify complex expressions and arrive at the correct answer.