An Expression Is Shown: $7.9 \times 10^6 - 6.5 \times 10^6$Which Expression Is Equivalent?A. $14.4 \times 10^6$B. $1 \times 10^6$C. $1.4 \times 10^6$

Introduction to 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. This notation is commonly used in mathematics, physics, and engineering to simplify calculations and make it easier to understand and compare large numbers.

Understanding the Given Expression

The given expression is $7.9 \times 10^6 - 6.5 \times 10^6$. This expression involves the subtraction of two numbers in scientific notation. To evaluate this expression, we need to understand the concept of subtracting numbers in scientific notation.

Subtracting Numbers in Scientific Notation

When subtracting numbers in scientific notation, we need to follow a specific procedure. The procedure involves subtracting the coefficients (the numbers in front of the powers of 10) and then subtracting the powers of 10. However, if the powers of 10 are different, we need to adjust the coefficients accordingly.

Evaluating the Given Expression

Let's evaluate the given expression $7.9 \times 10^6 - 6.5 \times 10^6$. Since the powers of 10 are the same, we can simply subtract the coefficients. Therefore, the expression becomes $7.9 - 6.5 = 1.4$. However, we need to keep the power of 10 the same, which is $10^6$. Therefore, the final expression is $1.4 \times 10^6$.

Comparing the Options

Now that we have evaluated the given expression, let's compare it with the options provided. Option A is $14.4 \times 10^6$, which is not equivalent to the given expression. Option B is $1 \times 10^6$, which is also not equivalent. Option C is $1.4 \times 10^6$, which is equivalent to the given expression.

Conclusion

In conclusion, the expression $7.9 \times 10^6 - 6.5 \times 10^6$ is equivalent to $1.4 \times 10^6$. This is because we can simply subtract the coefficients and keep the power of 10 the same. Therefore, the correct answer is option C, $1.4 \times 10^6$.

Frequently Asked Questions

• What is scientific notation?
• How do we subtract numbers in scientific notation?
• What is the correct answer to the given expression?

Answers to Frequently Asked Questions

• Scientific notation is a way of expressing very large or very small numbers in a more manageable form.
• To subtract numbers in scientific notation, we need to follow a specific procedure, which involves subtracting the coefficients and then subtracting the powers of 10.
• The correct answer to the given expression is $1.4 \times 10^6$.

Final Thoughts

In conclusion, the expression $7.9 \times 10^6 - 6.5 \times 10^6$ is equivalent to $1.4 \times 10^6$. This is because we can simply subtract the coefficients and keep the power of 10 the same. Therefore, the correct answer is option C, $1.4 \times 10^6$.

Introduction to 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. This notation is commonly used in mathematics, physics, and engineering to simplify calculations and make it easier to understand and compare large numbers.

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.

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

A: To express a number in 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.

Q: What is the power of 10 in scientific notation?

A: The power of 10 in scientific notation is the exponent that is multiplied by the number between 1 and 10. It can be positive or negative, depending on the direction of 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 a specific procedure. You need to add or subtract the coefficients (the numbers in front of the powers of 10) and then add or subtract the powers of 10.

Q: What is the difference between positive and negative exponents in scientific notation?

A: A positive exponent in scientific notation means that the decimal point is moved to the right, while a negative exponent means that the decimal point is moved to the left.

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 then add or subtract the powers of 10.

Q: What is the correct order of operations in scientific notation?

A: The correct order of operations in scientific notation is:

1. Parentheses
2. Exponents
3. Multiplication and Division
4. Addition and Subtraction

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 the power of 10.

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, and then multiply the number by a power of 10.

Conclusion

In conclusion, scientific notation is a powerful tool for expressing very large or very small numbers in a more manageable form. By understanding the concept of scientific notation and how to apply it, you can simplify calculations and make it easier to understand and compare large numbers.

Final Thoughts

Scientific notation is a fundamental concept in mathematics, physics, and engineering. By mastering the concept of scientific notation, you can improve your understanding of complex mathematical and scientific concepts and make it easier to solve problems and make calculations.

Additional Resources

• Scientific Notation Tutorial
• Scientific Notation Practice Problems
• Scientific Notation Calculator

Frequently Asked Questions

• What is scientific notation?
• How do I express a number in scientific notation?
• What is the power of 10 in scientific notation?
• How do I add or subtract numbers in scientific notation?
• What is the difference between positive and negative exponents in scientific notation?
• How do I multiply or divide numbers in scientific notation?
• What is the correct order of operations in scientific notation?
• How do I convert a number from scientific notation to standard notation?
• How do I convert a number from standard notation to scientific notation?

Answers to Frequently Asked Questions

• Scientific notation is a way of expressing very large or very small numbers in a more manageable form.
• To express a number in scientific notation, you need to move the decimal point to the left or right until you have a number between 1 and 10, and then multiply the number by a power of 10.
• The power of 10 in scientific notation is the exponent that is multiplied by the number between 1 and 10.
• To add or subtract numbers in scientific notation, you need to add or subtract the coefficients (the numbers in front of the powers of 10) and then add or subtract the powers of 10.
• A positive exponent in scientific notation means that the decimal point is moved to the right, while a negative exponent means that the decimal point is moved to the left.
• 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 then add or subtract the powers of 10.
• The correct order of operations in scientific notation is: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
• To convert a number from scientific notation to standard notation, you need to multiply the number by the power of 10.
• 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, and then multiply the number by a power of 10.