Find The Difference Of $6.761 \times 10^{12}$ And $4.1 \times 10^{12}$.A. \$2.661 \times 10^0$[/tex\]B. $6.351 \times 10^0$C. $2.661 \times 10^{12}$D. \$6.351 \times 10^{12}$[/tex\]

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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 how to find the difference of two large numbers in scientific notation.

Understanding Scientific Notation

Scientific notation is a way of expressing numbers in the form a × 10^n, where a is a number between 1 and 10, and n is an integer. For example, the number 456,000 can be expressed in scientific notation as 4.56 × 10^5.

Finding the Difference of Two Numbers in Scientific Notation

To find the difference of two numbers in scientific notation, we need to first express both numbers in the same form. We can do this by converting both numbers to decimal form and then subtracting the smaller number from the larger number.

Example 1: Finding the Difference of Two Numbers in Scientific Notation

Let's consider the two numbers 6.761 × 10^12 and 4.1 × 10^12. To find the difference of these two numbers, we need to first express both numbers in decimal form.

Step 1: Convert the Numbers to Decimal Form

To convert the numbers to decimal form, we need to multiply the coefficient (the number in front of the power of 10) by the power of 10.

For the first number, 6.761 × 10^12, we can convert it to decimal form by multiplying 6.761 by 10^12.

6.761 × 10^12 = 6.761 × 10^12

For the second number, 4.1 × 10^12, we can convert it to decimal form by multiplying 4.1 by 10^12.

4.1 × 10^12 = 4.1 × 10^12

Step 2: Subtract the Smaller Number from the Larger Number

Now that we have both numbers in decimal form, we can subtract the smaller number from the larger number to find the difference.

6.761 × 10^12 - 4.1 × 10^12 = 2.661 × 10^12

Conclusion

In this article, we have explored how to find the difference of two large numbers in scientific notation. We have seen that to find the difference of two numbers in scientific notation, we need to first express both numbers in the same form, and then subtract the smaller number from the larger number. We have also seen that the difference of two numbers in scientific notation can be expressed in the form a × 10^n, where a is a number between 1 and 10, and n is an integer.

Answer

The correct answer is C. $2.661 \times 10^{12}$.

Frequently Asked Questions

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 find the difference of two numbers in scientific notation?

A: To find the difference of two numbers in scientific notation, you need to first express both numbers in the same form, and then subtract the smaller number from the larger number.

Q: What is the difference between 6.761 × 10^12 and 4.1 × 10^12?

A: The difference between 6.761 × 10^12 and 4.1 × 10^12 is 2.661 × 10^12.

References

Keywords

  • Scientific notation
  • Difference of two numbers in scientific notation
  • Large numbers
  • Decimal form
  • Power of 10
  • Coefficient
  • Subtraction
  • Larger number
  • Smaller number

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Scientific notation is a powerful tool for expressing very large or very small numbers in a more manageable form. However, it can be confusing to understand and work with, especially for those who are new to the concept. In this article, we will answer some of the most frequently asked questions about scientific notation.

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.

Example

The number 456,000 can be expressed in scientific notation as 4.56 × 10^5.

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

A: To convert a number 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 a power of 10 that is equal to the number of places you moved the decimal point.

Example

To convert the number 456,000 to scientific notation, you would move the decimal point 5 places to the left, resulting in 4.56. Then, you would multiply 4.56 by 10^5.

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

A: To add or subtract numbers in scientific notation, you need to first make sure that the numbers have the same exponent. If they do not, you need to convert them to have the same exponent. Then, you can add or subtract the numbers as you would with regular numbers.

Example

To add the numbers 3.4 × 10^2 and 2.1 × 10^2, you would first convert them to have the same exponent. You would do this by multiplying 3.4 × 10^2 by 10^0 and 2.1 × 10^2 by 10^0. Then, you would add the numbers: 3.4 × 10^2 + 2.1 × 10^2 = 5.5 × 10^2.

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.

Example

To multiply the numbers 3.4 × 10^2 and 2.1 × 10^3, you would multiply the coefficients: 3.4 × 2.1 = 7.14. Then, you would add the exponents: 2 + 3 = 5. The result is 7.14 × 10^5.

Q: What is the difference between 6.761 × 10^12 and 4.1 × 10^12?

A: The difference between 6.761 × 10^12 and 4.1 × 10^12 is 2.661 × 10^12.

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

A: To convert a number from scientific notation to decimal form, you need to multiply the coefficient (the number in front of the power of 10) by the power of 10.

Example

To convert the number 4.56 × 10^5 to decimal form, you would multiply 4.56 by 10^5.

Q: What is the purpose of scientific notation?

A: The purpose of scientific notation is to express very large or very small numbers in a more manageable form. It allows us to work with numbers that are too large or too small to be expressed in regular decimal form.

Q: When should I use scientific notation?

A: You should use scientific notation when you need to express very large or very small numbers. It is particularly useful in scientific and mathematical applications where large or small numbers are common.

Q: How do I choose the correct exponent when converting a number to scientific notation?

A: When converting a number to scientific notation, you need to choose an exponent that is a multiple of 3. This will ensure that the number is expressed in the simplest form possible.

Example

To convert the number 456,000 to scientific notation, you would move the decimal point 5 places to the left, resulting in 4.56. Then, you would multiply 4.56 by 10^5.

Q: What are some common mistakes to avoid when working with scientific notation?

A: Some common mistakes to avoid when working with scientific notation include:

  • Not following the rules for adding and subtracting numbers in scientific notation
  • Not following the rules for multiplying and dividing numbers in scientific notation
  • Not converting numbers to have the same exponent before adding or subtracting them
  • Not choosing the correct exponent when converting a number to scientific notation

By following these rules and avoiding common mistakes, you can work confidently with scientific notation and express very large or very small numbers in a more manageable form.

Keywords

  • Scientific notation
  • Decimal form
  • Power of 10
  • Coefficient
  • Exponent
  • Adding and subtracting numbers in scientific notation
  • Multiplying and dividing numbers in scientific notation
  • Converting numbers to scientific notation
  • Choosing the correct exponent
  • Common mistakes to avoid