List The Following Numbers In Order From Least To Greatest: $2.8, 2.8 \times 10^2, 28 \times 10^{-3}, 28 \times 10^4, 28 \times 10^{-5}$.A. $2.8, 28 \times 10^2, 28 \times 10^{-3}, 28 \times 10^4, 28 \times 10^{-5}$B. $28 \times

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Understanding Scientific Notation

Scientific notation is a way of expressing numbers in the form of a product of a number between 1 and 10 and a power of 10. This notation is commonly used in mathematics and science to represent very large or very small numbers in a more compact and manageable form. In this article, we will explore how to order numbers in scientific notation from least to greatest.

The Numbers to be Ordered

The numbers to be ordered are:

  • 2.82.8
  • 2.8×1022.8 \times 10^2
  • 28×10−328 \times 10^{-3}
  • 28×10428 \times 10^4
  • 28×10−528 \times 10^{-5}

Ordering the Numbers

To order these numbers from least to greatest, we need to compare their values. We can do this by converting each number to a decimal form.

  • 2.8=2.8×1002.8 = 2.8 \times 10^0
  • 2.8×102=2.8×102×100=2.8×1022.8 \times 10^2 = 2.8 \times 10^2 \times 10^0 = 2.8 \times 10^2
  • 28×10−3=28×10−3×100=0.02828 \times 10^{-3} = 28 \times 10^{-3} \times 10^0 = 0.028
  • 28×104=28×104×100=280,00028 \times 10^4 = 28 \times 10^4 \times 10^0 = 280,000
  • 28×10−5=28×10−5×100=0.00002828 \times 10^{-5} = 28 \times 10^{-5} \times 10^0 = 0.000028

Now that we have converted each number to a decimal form, we can easily compare their values and order them from least to greatest.

The Correct Order

The correct order from least to greatest is:

  • 0.0000280.000028
  • 0.0280.028
  • 2.82.8
  • 2.8×102=2802.8 \times 10^2 = 280
  • 28×104=280,00028 \times 10^4 = 280,000

Therefore, the correct answer is:

A. 0.000028,0.028,2.8,280,280,0000.000028, 0.028, 2.8, 280, 280,000

Conclusion

Ordering numbers in scientific notation can be a bit tricky, but with the right approach, it can be done easily. By converting each number to a decimal form, we can compare their values and order them from least to greatest. In this article, we have seen how to order numbers in scientific notation and have learned the correct order for the given numbers.

Frequently Asked Questions

  • Q: What is scientific notation? A: Scientific notation is a way of expressing numbers in the form of a product of a number between 1 and 10 and a power of 10.
  • Q: How do I order numbers in scientific notation? A: To order numbers in scientific notation, convert each number to a decimal form and compare their values.
  • Q: What is the correct order for the given numbers? A: The correct order is 0.000028,0.028,2.8,280,280,0000.000028, 0.028, 2.8, 280, 280,000.
    Scientific Notation Q&A ==========================

Frequently Asked Questions

Q: What is scientific notation?

A: Scientific notation is a way of expressing numbers in the form of a product of a number between 1 and 10 and a power of 10. This notation is commonly used in mathematics and science to represent very large or very small numbers in a more compact and manageable form.

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

A: To convert a number to scientific notation, follow these steps:

  1. Move the decimal point: Move the decimal point to the left until you have a number between 1 and 10.
  2. Determine the exponent: The number of places you moved the decimal point is the exponent. If you moved it to the left, the exponent is positive. If you moved it to the right, the exponent is negative.
  3. Write the number in scientific notation: Write the number in the form of a product of a number between 1 and 10 and a power of 10.

Q: How do I order numbers in scientific notation?

A: To order numbers in scientific notation, convert each number to a decimal form and compare their values. You can also compare the exponents to determine the order.

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

A: Standard notation is the usual way of writing numbers, without any special notation. Scientific notation, on the other hand, is a way of expressing numbers in a more compact and manageable form, using a product of a number between 1 and 10 and a power of 10.

Q: When should I use scientific notation?

A: You should use scientific notation when:

  • You need to represent very large or very small numbers.
  • You need to perform calculations with numbers that have many digits.
  • You need to express numbers in a more compact and manageable form.

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

A: To multiply and divide numbers in scientific notation, follow these rules:

  • Multiply the numbers: Multiply the numbers as if they were in standard notation.
  • Add the exponents: Add the exponents of the two numbers.
  • Write the result in scientific notation: Write the result in the form of a product of a number between 1 and 10 and a power of 10.

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

A: To add and subtract numbers in scientific notation, follow these rules:

  • Make the exponents the same: Make the exponents of the two numbers the same by adding or subtracting the same amount to both exponents.
  • Add or subtract the numbers: Add or subtract the numbers as if they were in standard notation.
  • Write the result in scientific notation: Write the result in the form of a product of a number between 1 and 10 and a power of 10.

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:

  • Forgetting to move the decimal point: Make sure to move the decimal point to the left or right by the correct amount when converting a number to scientific notation.
  • Forgetting to add or subtract the exponents: Make sure to add or subtract the exponents correctly when multiplying or dividing numbers in scientific notation.
  • Forgetting to write the result in scientific notation: Make sure to write the result in the form of a product of a number between 1 and 10 and a power of 10.

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

A: To convert a number from scientific notation to standard notation, follow these steps:

  1. Multiply the number by the power of 10: Multiply the number by the power of 10.
  2. Move the decimal point: Move the decimal point to the right by the same amount as the exponent.

Q: What are some real-world applications of scientific notation?

A: Some real-world applications of scientific notation include:

  • Physics and engineering: Scientific notation is used to represent large and small numbers in physics and engineering, such as distances, velocities, and forces.
  • Chemistry: Scientific notation is used to represent large and small numbers in chemistry, such as atomic masses and molecular weights.
  • Computer science: Scientific notation is used to represent large and small numbers in computer science, such as memory addresses and file sizes.

Q: How do I use scientific notation in a calculator?

A: To use scientific notation in a calculator, follow these steps:

  1. Enter the number in scientific notation: Enter the number in the form of a product of a number between 1 and 10 and a power of 10.
  2. Use the calculator's scientific notation mode: Use the calculator's scientific notation mode to perform calculations with numbers in scientific notation.

Q: What are some common misconceptions about scientific notation?

A: Some common misconceptions about scientific notation include:

  • Scientific notation is only used for very large numbers: Scientific notation is used for both very large and very small numbers.
  • Scientific notation is only used in science and engineering: Scientific notation is used in many fields, including business, finance, and computer science.
  • Scientific notation is only used for numbers with many digits: Scientific notation is used for numbers with any number of digits.