The Distance From The Earth To The Moon Is About 239,000 Miles. Rewrite The Distance In Scientific Notation.A. $2.39 \times 10^5$ B. $23.9 \times 10^4$ C. $23.9 \times 10^{-4}$ D. $2.39 \times 10^{-5}$

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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 explore the concept of scientific notation and apply it to the distance from the Earth to the moon.

What is Scientific Notation?

Scientific notation is a method of expressing numbers as a product of a number between 1 and 10 and a power of 10. It is written in the form:

a × 10^n

where 'a' is the coefficient and 'n' is the exponent. The coefficient is a number between 1 and 10, and the exponent is a positive or negative integer.

Rewriting the Distance to the Moon in Scientific Notation

The distance from the Earth to the moon is approximately 239,000 miles. To rewrite this number in scientific notation, we need to express it as a product of a number between 1 and 10 and a power of 10.

Let's break down the number 239,000:

  • The coefficient is 239, which is between 1 and 10.
  • The exponent is the power of 10 that we need to multiply by the coefficient to get the original number.

To find the exponent, we can use the fact that 10^5 = 100,000. Since 239,000 is greater than 100,000, we need to multiply 100,000 by a number greater than 1 to get 239,000. This number is 2.39.

Therefore, the distance from the Earth to the moon in scientific notation is:

2.39 × 10^5

Comparing the Options

Now that we have rewritten the distance to the moon in scientific notation, let's compare it to the options provided:

A. 2.39×1052.39 \times 10^5 B. 23.9×10423.9 \times 10^4 C. 23.9×10−423.9 \times 10^{-4} D. 2.39×10−52.39 \times 10^{-5}

Only option A matches our calculation.

Conclusion

In this article, we have explored the concept of scientific notation and applied it to the distance from the Earth to the moon. We have shown that the correct scientific notation for the distance is 2.39 × 10^5. This demonstrates the importance of understanding scientific notation in mathematics and science.

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 is written in the form a × 10^n, where 'a' is the coefficient and 'n' is the exponent.

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

A: To convert a number to scientific notation, you need to express it as a product of a number between 1 and 10 and a power of 10. You can do this by breaking down the number into its coefficient and exponent.

Q: What is the distance from the Earth to the moon in scientific notation?

A: The distance from the Earth to the moon is approximately 239,000 miles, which is equal to 2.39 × 10^5 in scientific notation.

Q: Why is scientific notation important?

A: Scientific notation is important because it makes it easier to understand and work with very large or very small numbers. It is commonly used in mathematics, physics, and other scientific fields to simplify calculations and make it easier to understand complex concepts.

References

Additional Resources

Scientific notation is a powerful tool for expressing very large or very small numbers in a more manageable form. In this article, we will answer some frequently asked questions about scientific notation to help you better understand this concept.

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 written in the form a × 10^n, where 'a' is the coefficient and 'n' is the exponent.

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

A: To convert a number to scientific notation, you need to express it as a product of a number between 1 and 10 and a power of 10. You can do this by breaking down the number into its coefficient and exponent.

For example, let's convert the number 456,789 to scientific notation:

  • The coefficient is 4.56789, which is between 1 and 10.
  • The exponent is 5, since 10^5 = 100,000 and we need to multiply 100,000 by 4.56789 to get 456,789.

Therefore, the scientific notation for 456,789 is 4.56789 × 10^5.

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

A: To convert a number from scientific notation to standard form, you need to multiply the coefficient by the power of 10.

For example, let's convert the number 3.45 × 10^4 to standard form:

  • Multiply the coefficient (3.45) by the power of 10 (10^4): 3.45 × 10^4 = 34,500

Therefore, the standard form of 3.45 × 10^4 is 34,500.

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

A: Scientific notation and exponential notation are both used to express very large or very small numbers, but they are not the same thing.

Scientific notation is a specific way of expressing numbers in the form a × 10^n, where 'a' is the coefficient and 'n' is the exponent.

Exponential notation, on the other hand, is a more general way of expressing numbers in the form a^b, where 'a' is the base and 'b' is the exponent.

For example, the number 10^5 can be expressed in scientific notation as 1 × 10^5, but it can also be expressed in exponential notation as 10^5.

Q: When should I use scientific notation?

A: You should use scientific notation whenever you need to express very large or very small numbers in a more manageable form.

For example, if you are working with numbers that are too large or too small to be expressed in standard form, you may want to use scientific notation to simplify your calculations.

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

A: To add or subtract numbers in scientific notation, you need to follow the same rules as you would with standard numbers.

For example, let's add the numbers 2.5 × 10^3 and 1.2 × 10^3:

  • First, make sure the exponents are the same: 2.5 × 10^3 and 1.2 × 10^3 both have an exponent of 3.
  • Next, add the coefficients: 2.5 + 1.2 = 3.7
  • Finally, write the result in scientific notation: 3.7 × 10^3

Therefore, the result of adding 2.5 × 10^3 and 1.2 × 10^3 is 3.7 × 10^3.

Q: How do I multiply or divide numbers in scientific notation?

A: To multiply or divide numbers in scientific notation, you need to follow the same rules as you would with standard numbers.

For example, let's multiply the numbers 2.5 × 10^3 and 1.2 × 10^3:

  • First, multiply the coefficients: 2.5 × 1.2 = 3
  • Next, add the exponents: 3 + 3 = 6
  • Finally, write the result in scientific notation: 3 × 10^6

Therefore, the result of multiplying 2.5 × 10^3 and 1.2 × 10^3 is 3 × 10^6.

Conclusion

In this article, we have answered some frequently asked questions about scientific notation to help you better understand this concept. We have covered topics such as converting numbers to and from scientific notation, adding and subtracting numbers in scientific notation, and multiplying and dividing numbers in scientific notation.

Frequently Asked Questions

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

A: Scientific notation is a way of expressing very large or very small numbers in a more manageable form, while standard form is the usual way of writing numbers.

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

A: To convert a number from scientific notation to standard form, you need to multiply the coefficient by the power of 10.

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

A: Scientific notation is a specific way of expressing numbers in the form a × 10^n, while exponential notation is a more general way of expressing numbers in the form a^b.

Q: When should I use scientific notation?

A: You should use scientific notation whenever you need to express very large or very small numbers in a more manageable form.

References

Additional Resources