Express The Number In Decimal Notation.$8.81 \times 10^{-5}$$8.81 \times 10^{-5} =$$\square$

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Understanding Decimal Notation

Decimal notation is a way of expressing numbers using a decimal point. It is a fundamental concept in mathematics and is used to represent numbers in a more readable and understandable format. In decimal notation, numbers are expressed as a combination of digits, a decimal point, and an exponent. The exponent is used to indicate the power of 10 to which the number should be raised.

Expressing Numbers in 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. It is a convenient way to express very large or very small numbers. In scientific notation, numbers are expressed as a combination of a coefficient, a decimal point, and an exponent. The coefficient is a number between 1 and 10, and the exponent is a power of 10.

Converting Scientific Notation to Decimal Notation

To convert a number from scientific notation to decimal notation, we need to multiply the coefficient by the power of 10 indicated by the exponent. For example, if we have the number 8.81×10−58.81 \times 10^{-5}, we can convert it to decimal notation by multiplying the coefficient 8.81 by 10−510^{-5}.

Converting 8.81×10−58.81 \times 10^{-5} to Decimal Notation

To convert 8.81×10−58.81 \times 10^{-5} to decimal notation, we need to multiply the coefficient 8.81 by 10−510^{-5}. This can be done by moving the decimal point in the coefficient 5 places to the left and then multiplying by 1.

Step 1: Move the Decimal Point

To move the decimal point in the coefficient 5 places to the left, we need to add 5 zeros to the end of the coefficient. This gives us 8.81,000,000.

Step 2: Multiply by 1

We then multiply the coefficient 8.81,000,000 by 1. This gives us 8.81,000,000.

Step 3: Write the Result

The result of multiplying the coefficient 8.81,000,000 by 10−510^{-5} is 0.0000881.

Conclusion

In conclusion, we have seen how to convert a number from scientific notation to decimal notation. We have used the example of 8.81×10−58.81 \times 10^{-5} to illustrate the process. By following the steps outlined above, we can convert any number from scientific notation to decimal notation.

Example Problems

Problem 1

Express 4.23×1034.23 \times 10^{3} in decimal notation.

Solution

To express 4.23×1034.23 \times 10^{3} in decimal notation, we need to multiply the coefficient 4.23 by 10310^{3}. This can be done by moving the decimal point in the coefficient 3 places to the right and then multiplying by 1.

Step 1: Move the Decimal Point

To move the decimal point in the coefficient 3 places to the right, we need to add 3 zeros to the end of the coefficient. This gives us 4.23,000.

Step 2: Multiply by 1

We then multiply the coefficient 4.23,000 by 1. This gives us 4,230.

Step 3: Write the Result

The result of multiplying the coefficient 4,230 by 10310^{3} is 4,230.

Problem 2

Express 9.56×10−29.56 \times 10^{-2} in decimal notation.

Solution

To express 9.56×10−29.56 \times 10^{-2} in decimal notation, we need to multiply the coefficient 9.56 by 10−210^{-2}. This can be done by moving the decimal point in the coefficient 2 places to the left and then multiplying by 1.

Step 1: Move the Decimal Point

To move the decimal point in the coefficient 2 places to the left, we need to add 2 zeros to the end of the coefficient. This gives us 9.56,00.

Step 2: Multiply by 1

We then multiply the coefficient 9.56,00 by 1. This gives us 0.0956.

Step 3: Write the Result

The result of multiplying the coefficient 0.0956 by 10−210^{-2} is 0.0956.

Conclusion

In conclusion, we have seen how to convert numbers from scientific notation to decimal notation. We have used the examples of 4.23×1034.23 \times 10^{3} and 9.56×10−29.56 \times 10^{-2} to illustrate the process. By following the steps outlined above, we can convert any number from scientific notation to decimal notation.

Key Takeaways

  • Decimal notation is a way of expressing numbers using a decimal point.
  • 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.
  • To convert a number from scientific notation to decimal notation, we need to multiply the coefficient by the power of 10 indicated by the exponent.
  • We can move the decimal point in the coefficient by adding or subtracting zeros.
  • We can multiply the coefficient by 1 to get the result.

Final Thoughts

In conclusion, decimal notation is an important concept in mathematics that allows us to express numbers in a more readable and understandable format. By understanding how to convert numbers from scientific notation to decimal notation, we can perform calculations and solve problems more easily. We hope that this article has provided you with a clear understanding of decimal notation and how to convert numbers from scientific notation to decimal notation.

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Q1: What is decimal notation?

A1: Decimal notation is a way of expressing numbers using a decimal point. It is a fundamental concept in mathematics and is used to represent numbers in a more readable and understandable format.

Q2: What is scientific notation?

A2: 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. It is a convenient way to express very large or very small numbers.

Q3: How do I convert a number from scientific notation to decimal notation?

A3: To convert a number from scientific notation to decimal notation, you need to multiply the coefficient by the power of 10 indicated by the exponent. You can do this by moving the decimal point in the coefficient by the number of places indicated by the exponent.

Q4: What is the difference between decimal notation and scientific notation?

A4: The main difference between decimal notation and scientific notation is the way numbers are expressed. In decimal notation, numbers are expressed as a combination of digits and a decimal point. In scientific notation, numbers are expressed as a product of a number between 1 and 10 and a power of 10.

Q5: How do I move the decimal point in a number?

A5: To move the decimal point in a number, you need to add or subtract zeros from the end of the number. If you want to move the decimal point to the right, you need to add zeros to the end of the number. If you want to move the decimal point to the left, you need to subtract zeros from the end of the number.

Q6: What is the coefficient in scientific notation?

A6: The coefficient in scientific notation is a number between 1 and 10 that is multiplied by a power of 10 to express a number in scientific notation.

Q7: What is the exponent in scientific notation?

A7: The exponent in scientific notation is a power of 10 that is multiplied by the coefficient to express a number in scientific notation.

Q8: How do I convert a number from decimal notation to scientific notation?

A8: To convert a number from decimal notation to scientific notation, you need to express the number as a product of a number between 1 and 10 and a power of 10. You can do this by moving the decimal point in the number to the right or left until you get a number between 1 and 10.

Q9: What is the advantage of using scientific notation?

A9: The advantage of using scientific notation is that it allows us to express very large or very small numbers in a more readable and understandable format.

Q10: What is the disadvantage of using scientific notation?

A10: The disadvantage of using scientific notation is that it can be confusing for people who are not familiar with it.

Conclusion

In conclusion, decimal notation and scientific notation are two important concepts in mathematics that allow us to express numbers in a more readable and understandable format. By understanding how to convert numbers from decimal notation to scientific notation and vice versa, we can perform calculations and solve problems more easily.

Key Takeaways

  • Decimal notation is a way of expressing numbers using a decimal point.
  • 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.
  • To convert a number from scientific notation to decimal notation, you need to multiply the coefficient by the power of 10 indicated by the exponent.
  • To convert a number from decimal notation to scientific notation, you need to express the number as a product of a number between 1 and 10 and a power of 10.
  • The advantage of using scientific notation is that it allows us to express very large or very small numbers in a more readable and understandable format.

Final Thoughts

In conclusion, decimal notation and scientific notation are two important concepts in mathematics that allow us to express numbers in a more readable and understandable format. By understanding how to convert numbers from decimal notation to scientific notation and vice versa, we can perform calculations and solve problems more easily. We hope that this article has provided you with a clear understanding of decimal notation and scientific notation.