Evaluate And Express Your Answer In Scientific Notation: 7.9 × 10 5 + 5.4 × 10 5 7.9 \times 10^5 + 5.4 \times 10^5 7.9 × 1 0 5 + 5.4 × 1 0 5

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Introduction

Scientific notation is a way of expressing very large or very small numbers in a more manageable form. It is commonly used in mathematics, physics, and other scientific fields to simplify calculations and make it easier to understand complex concepts. In this article, we will evaluate and express the answer in scientific notation for the given expression: $7.9 \times 10^5 + 5.4 \times 10^5$.

Understanding Scientific Notation

Scientific notation is a way of expressing numbers in the form $a \times 10^b$, where $a$ is a number between 1 and 10, and $b$ is an integer. This notation is useful for expressing very large or very small numbers in a more compact form. For example, the number 456,000 can be expressed in scientific notation as $4.56 \times 10^5$.

Evaluating the Expression

To evaluate the expression $7.9 \times 10^5 + 5.4 \times 10^5$, we need to first add the two numbers. However, since they are in scientific notation, we need to make sure that they have the same exponent. In this case, both numbers have an exponent of $10^5$, so we can add them directly.

Adding Numbers in Scientific Notation

When adding numbers in scientific notation, we need to make sure that they have the same exponent. If they do, we can add the coefficients (the numbers in front of the exponent) and keep the same exponent. In this case, we have:

$7.9 \times 10^5 + 5.4 \times 10^5$

Since both numbers have the same exponent, we can add the coefficients:

$7.9 + 5.4 = 13.3$

So, the expression becomes:

$13.3 \times 10^5$

Expressing the Answer in Scientific Notation

Now that we have evaluated the expression, we need to express the answer in scientific notation. Since the answer is $13.3 \times 10^5$, we can express it in scientific notation as:

$1.33 \times 10^6$

This is because we can rewrite $13.3$ as $1.33 \times 10^1$, and then multiply the exponents to get $10^6$.

Conclusion

In conclusion, we have evaluated and expressed the answer in scientific notation for the given expression: $7.9 \times 10^5 + 5.4 \times 10^5$. We first added the two numbers in scientific notation, and then expressed the answer in scientific notation. The final answer is $1.33 \times 10^6$.

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.
• How do I add numbers in scientific notation? When adding numbers in scientific notation, make sure that they have the same exponent. If they do, add the coefficients and keep the same exponent.
• How do I express a number in scientific notation? To express a number in scientific notation, rewrite it in the form $a \times 10^b$, where $a$ is a number between 1 and 10, and $b$ is an integer.

Examples

• Express the number 456,000 in scientific notation. $4.56 \times 10^5$
• Express the number 0.00045 in scientific notation. $4.5 \times 10^{-4}$
• Evaluate the expression $2.1 \times 10^4 + 1.8 \times 10^4$. $3.9 \times 10^4$

Applications

Scientific notation is commonly used in mathematics, physics, and other scientific fields to simplify calculations and make it easier to understand complex concepts. It is also used in engineering, computer science, and other fields where large or small numbers are encountered.

References

• "Scientific Notation" by Math Is Fun
• "Scientific Notation" by Khan Academy
• "Scientific Notation" by Wolfram MathWorld
  

Introduction

Scientific notation is a powerful tool used to simplify calculations and make it easier to understand complex concepts. However, it can be a bit tricky to work with, especially when it comes to adding and subtracting numbers in scientific notation. In this article, we will answer some of the most frequently asked questions about scientific notation.

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 is commonly used in mathematics, physics, and other scientific fields to simplify calculations and make it easier to understand complex concepts.

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

A: To express a number in scientific notation, rewrite it in the form $a \times 10^b$, where $a$ is a number between 1 and 10, and $b$ is an integer. For example, the number 456,000 can be expressed in scientific notation as $4.56 \times 10^5$.

Q: How do I add numbers in scientific notation?

A: When adding numbers in scientific notation, make sure that they have the same exponent. If they do, add the coefficients and keep the same exponent. For example, $2.1 \times 10^4 + 1.8 \times 10^4$ can be added as follows:

$2.1 + 1.8 = 3.9$

So, the expression becomes:

$3.9 \times 10^4$

Q: How do I subtract numbers in scientific notation?

A: When subtracting numbers in scientific notation, make sure that they have the same exponent. If they do, subtract the coefficients and keep the same exponent. For example, $2.1 \times 10^4 - 1.8 \times 10^4$ can be subtracted as follows:

$2.1 - 1.8 = 0.3$

So, the expression becomes:

$0.3 \times 10^4$

Q: Can I multiply numbers in scientific notation?

A: Yes, you can multiply numbers in scientific notation. When multiplying numbers in scientific notation, multiply the coefficients and add the exponents. For example, $(2.1 \times 10^4) \times (1.8 \times 10^4)$ can be multiplied as follows:

$2.1 \times 1.8 = 3.78$

$4 + 4 = 8$

So, the expression becomes:

$3.78 \times 10^8$

Q: Can I divide numbers in scientific notation?

A: Yes, you can divide numbers in scientific notation. When dividing numbers in scientific notation, divide the coefficients and subtract the exponents. For example, $(2.1 \times 10^4) \div (1.8 \times 10^4)$ can be divided as follows:

$2.1 \div 1.8 = 1.167$

$4 - 4 = 0$

So, the expression becomes:

$1.167 \times 10^0$

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

A: Scientific notation and standard notation are two different ways of expressing numbers. Standard notation is the way we normally write numbers, with a decimal point and a whole number part. Scientific notation, on the other hand, is a way of expressing numbers in a more compact form, using a coefficient and an exponent.

Q: When should I use scientific notation?

A: You should use scientific notation when working with very large or very small numbers. It is also useful when simplifying calculations and making it easier to understand complex concepts.

Examples

• Express the number 456,000 in scientific notation. $4.56 \times 10^5$
• Express the number 0.00045 in scientific notation. $4.5 \times 10^{-4}$
• Evaluate the expression $2.1 \times 10^4 + 1.8 \times 10^4$. $3.9 \times 10^4$
• Multiply the numbers $(2.1 \times 10^4) \times (1.8 \times 10^4)$. $3.78 \times 10^8$
• Divide the numbers $(2.1 \times 10^4) \div (1.8 \times 10^4)$. $1.167 \times 10^0$

Applications

Scientific notation is commonly used in mathematics, physics, and other scientific fields to simplify calculations and make it easier to understand complex concepts. It is also used in engineering, computer science, and other fields where large or small numbers are encountered.

References

• "Scientific Notation" by Math Is Fun
• "Scientific Notation" by Khan Academy
• "Scientific Notation" by Wolfram MathWorld