Evaluate The Expression And Express Your Answer In Scientific Notation.$9.9 \times 10^{-2} + 7.9 \times 10^{-4}$Answer: $\square \times 10^{\square}$

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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 engineering to simplify calculations and make it easier to understand complex concepts. In this article, we will evaluate the expression 9.9×10−2+7.9×10−49.9 \times 10^{-2} + 7.9 \times 10^{-4} and express the answer in scientific notation.

Understanding Scientific Notation

Scientific notation is a way of expressing numbers as a product of a number between 1 and 10 and a power of 10. For example, the number 456 can be expressed in scientific notation as 4.56×1024.56 \times 10^2. Similarly, the number 0.003 can be expressed in scientific notation as 3×10−33 \times 10^{-3}.

Evaluating the Expression

To evaluate the expression 9.9×10−2+7.9×10−49.9 \times 10^{-2} + 7.9 \times 10^{-4}, we need to first convert both numbers to the same power of 10. We can do this by multiplying the first number by 10210^2 and the second number by 10210^2.

# Import necessary modules
import math

# Define variables
num1 = 9.9 * (10 ** -2)
num2 = 7.9 * (10 ** -4)

# Convert both numbers to the same power of 10
num1 = num1 * (10 ** 2)
num2 = num2 * (10 ** 2)

Simplifying the Expression

Now that both numbers are in the same power of 10, we can add them together.

# Add both numbers together
result = num1 + num2

Expressing the Answer in Scientific Notation

To express the answer in scientific notation, we need to convert the result to a number between 1 and 10 and a power of 10.

# Convert the result to scientific notation
result = result / (10 ** 2)

Conclusion

In this article, we evaluated the expression 9.9×10−2+7.9×10−49.9 \times 10^{-2} + 7.9 \times 10^{-4} and expressed the answer in scientific notation. We first converted both numbers to the same power of 10, then added them together, and finally expressed the result in scientific notation.

Final Answer

The final answer is 0.0999×100\boxed{0.0999 \times 10^0}.

Discussion

Scientific notation is a powerful tool for simplifying complex calculations and making it easier to understand complex concepts. By expressing numbers in scientific notation, we can make it easier to perform calculations and understand the relationships between different numbers.

Example Use Cases

Scientific notation has many practical applications in mathematics, physics, and engineering. For example, it can be used to express the speed of light as 3×1083 \times 10^8 meters per second, or the distance between the Earth and the Sun as 1.5×10111.5 \times 10^{11} meters.

Tips and Tricks

When working with scientific notation, it's essential to remember that the power of 10 is the exponent, not the coefficient. For example, the number 4.56×1024.56 \times 10^2 is not equal to 4.5624.56^2.

Common Mistakes

One common mistake when working with scientific notation is to confuse the power of 10 with the coefficient. For example, the number 4.56×1024.56 \times 10^2 is not equal to 4.5624.56^2.

Conclusion

In conclusion, scientific notation is a powerful tool for simplifying complex calculations and making it easier to understand complex concepts. By expressing numbers in scientific notation, we can make it easier to perform calculations and understand the relationships between different numbers.

Final Thoughts

Scientific notation is a fundamental concept in mathematics, physics, and engineering. By mastering scientific notation, we can simplify complex calculations and make it easier to understand complex concepts.

References

  • [1] "Scientific Notation" by Math Is Fun
  • [2] "Scientific Notation" by Khan Academy
  • [3] "Scientific Notation" by Wolfram MathWorld

Further Reading

For further reading on scientific notation, we recommend the following resources:

  • [1] "Scientific Notation" by Math Is Fun
  • [2] "Scientific Notation" by Khan Academy
  • [3] "Scientific Notation" by Wolfram MathWorld

FAQs

Q: What is scientific notation?

A: Scientific notation is a way of expressing numbers 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 convert it to a number between 1 and 10 and a power of 10.

Q: What are some common applications of scientific notation?

A: Scientific notation has many practical applications in mathematics, physics, and engineering, such as expressing the speed of light or the distance between the Earth and the Sun.

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

A: One common mistake to avoid is confusing the power of 10 with the coefficient.

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Frequently Asked Questions

Q: What is scientific notation?

A: Scientific notation is a way of expressing numbers as a product of a number between 1 and 10 and a power of 10. It is commonly used in mathematics, physics, and engineering 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, you need to convert it to a number between 1 and 10 and a power of 10. For example, the number 456 can be expressed in scientific notation as 4.56×1024.56 \times 10^2.

Q: What are some common applications of scientific notation?

A: Scientific notation has many practical applications in mathematics, physics, and engineering, such as expressing the speed of light as 3×1083 \times 10^8 meters per second, or the distance between the Earth and the Sun as 1.5×10111.5 \times 10^{11} meters.

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

A: One common mistake to avoid is confusing the power of 10 with the coefficient. For example, the number 4.56×1024.56 \times 10^2 is not equal to 4.5624.56^2.

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 or divide by 10 to the power of the number of places you moved the decimal point.

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 10 to the power of the exponent, and then move the decimal point to the right or left by the number of places equal to the exponent.

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

A: Scientific notation is a way of expressing numbers as a product of a number between 1 and 10 and a power of 10, while exponential notation is a way of expressing numbers as a product of a number and a power of a base number, such as 232^3.

Q: Can I use scientific notation with negative exponents?

A: Yes, you can use scientific notation with negative exponents. For example, the number 0.003 can be expressed in scientific notation as 3×10−33 \times 10^{-3}.

Q: Can I use scientific notation with decimal exponents?

A: Yes, you can use scientific notation with decimal exponents. For example, the number 456.789 can be expressed in scientific notation as 4.56789×1024.56789 \times 10^2.

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, and then add or subtract the coefficients.

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 and add or subtract the exponents.

Additional Resources

For further reading on scientific notation, we recommend the following resources:

  • [1] "Scientific Notation" by Math Is Fun
  • [2] "Scientific Notation" by Khan Academy
  • [3] "Scientific Notation" by Wolfram MathWorld

Conclusion

In conclusion, scientific notation is a powerful tool for simplifying complex calculations and making it easier to understand complex concepts. By mastering scientific notation, you can simplify calculations and make it easier to understand complex concepts.

Final Thoughts

Scientific notation is a fundamental concept in mathematics, physics, and engineering. By mastering scientific notation, you can simplify calculations and make it easier to understand complex concepts.

References

  • [1] "Scientific Notation" by Math Is Fun
  • [2] "Scientific Notation" by Khan Academy
  • [3] "Scientific Notation" by Wolfram MathWorld

FAQs

Q: What is the purpose of scientific notation?

A: The purpose of scientific notation is to simplify complex calculations and make it easier to understand complex concepts.

Q: How do I use scientific notation in real-life situations?

A: You can use scientific notation in real-life situations such as expressing the speed of light, the distance between the Earth and the Sun, or the number of atoms in a molecule.

Q: What are some common applications of scientific notation in science and engineering?

A: Scientific notation has many practical applications in science and engineering, such as expressing the speed of light, the distance between the Earth and the Sun, or the number of atoms in a molecule.

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 or divide by 10 to the power of the number of places you moved the decimal point.

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 10 to the power of the exponent, and then move the decimal point to the right or left by the number of places equal to the exponent.