A Solution Has A Hydrogen Ion Concentration Of 0.00000725 Moles Per Liter. Write The Concentration In Scientific Notation.(b) A Fin Whale Can Weigh Up To $2.6 \times 10^5$ Pounds. Write This Number In Standard Notation.

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Introduction

Scientific notation and standard notation are two ways of expressing numbers in a more manageable and readable format. Scientific notation is a way of expressing numbers as a product of a number between 1 and 10 and a power of 10, while standard notation is the way we normally write numbers. In this article, we will explore how to express a solution of hydrogen ions and the weight of a fin whale in both scientific and standard notation.

Expressing the Concentration of Hydrogen Ions in Scientific Notation

The concentration of a solution is a measure of the amount of a substance dissolved in a given volume of a solvent. In this case, we are given the concentration of a solution of hydrogen ions as 0.00000725 moles per liter. To express this concentration in scientific notation, we need to rewrite it as a product of a number between 1 and 10 and a power of 10.

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 scientific and engineering applications where large or small numbers need to be expressed in a more manageable format.

To express the concentration of hydrogen ions in scientific notation, we can move the decimal point to the right until we have a number between 1 and 10. In this case, we can move the decimal point 6 places to the right to get 7.25. Since we moved the decimal point 6 places to the right, we need to multiply the number by 10^(-6) to get the correct value.

Therefore, the concentration of hydrogen ions in scientific notation is:

7.25 x 10^(-6) moles per liter

Expressing the Weight of a Fin Whale in Standard Notation

The weight of a fin whale is given as 2.6 x 10^5 pounds. To express this weight in standard notation, we need to rewrite it as a single number without any exponents.

Standard notation is the way we normally write numbers. It is the opposite of scientific notation, where numbers are expressed as a product of a number between 1 and 10 and a power of 10.

To express the weight of a fin whale in standard notation, we can multiply the number by the power of 10. In this case, we need to multiply 2.6 by 10^5.

10^5 = 100,000

Therefore, the weight of a fin whale in standard notation is:

2.6 x 100,000 = 260,000 pounds

Conclusion

In conclusion, scientific notation and standard notation are two ways of expressing numbers in a more manageable and readable format. Scientific notation is a way of expressing numbers as a product of a number between 1 and 10 and a power of 10, while standard notation is the way we normally write numbers. By understanding how to express numbers in both scientific and standard notation, we can better understand and work with large and small numbers in a variety of applications.

Applications of Scientific and Standard Notation

Scientific and standard notation have a wide range of applications in various fields, including:

  • Chemistry: Scientific notation is commonly used in chemistry to express the concentration of solutions, the amount of substances, and the results of chemical reactions.
  • Physics: Scientific notation is used in physics to express the results of measurements, the values of physical constants, and the equations of motion.
  • Engineering: Scientific notation is used in engineering to express the results of calculations, the values of physical properties, and the specifications of materials and equipment.
  • Computer Science: Scientific notation is used in computer science to express the results of calculations, the values of variables, and the specifications of algorithms and data structures.

Examples of Scientific and Standard Notation

Here are some examples of scientific and standard notation:

  • Scientific notation: 3.45 x 10^(-2), 2.1 x 10^3, 4.8 x 10^(-5)
  • Standard notation: 0.0345, 2100, 0.000048

Tips for Converting Between Scientific and Standard Notation

Here are some tips for converting between scientific and standard notation:

  • Move the decimal point: To convert a number from scientific notation to standard notation, move the decimal point to the right until you have a number between 1 and 10.
  • Multiply by the power of 10: To convert a number from scientific notation to standard notation, multiply the number by the power of 10.
  • Divide by the power of 10: To convert a number from standard notation to scientific notation, divide the number by the power of 10.

Conclusion

In conclusion, scientific notation and standard notation are two ways of expressing numbers in a more manageable and readable format. By understanding how to express numbers in both scientific and standard notation, we can better understand and work with large and small numbers in a variety of applications.

Introduction

In our previous article, we explored the concept of scientific notation and standard notation, and how to express a solution of hydrogen ions and the weight of a fin whale in both formats. In this article, we will answer some frequently asked questions about scientific notation and standard notation.

Q&A

Q: What is the difference between scientific notation and standard 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 scientific and engineering applications where large or small numbers need to be expressed in a more manageable format. Standard notation, on the other hand, is the way we normally write numbers.

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

A: To convert a number from scientific notation to standard notation, move the decimal point to the right until you have a number between 1 and 10. Then, multiply the number by the power of 10.

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

A: To convert a number from standard notation to scientific notation, divide the number by the power of 10. Then, move the decimal point to the left until you have a number between 1 and 10.

Q: What is the purpose of scientific notation?

A: The purpose of scientific notation is to express numbers in a more manageable and readable format. It is commonly used in scientific and engineering applications where large or small numbers need to be expressed in a more manageable format.

Q: What are some examples of scientific notation?

A: Here are some examples of scientific notation:

  • 3.45 x 10^(-2)
  • 2.1 x 10^3
  • 4.8 x 10^(-5)

Q: What are some examples of standard notation?

A: Here are some examples of standard notation:

  • 0.0345
  • 2100
  • 0.000048

Q: How do I determine the power of 10 in scientific notation?

A: The power of 10 in scientific notation is determined by the number of places you need to move the decimal point to the right to get a number between 1 and 10.

Q: Can I use scientific notation with negative numbers?

A: Yes, you can use scientific notation with negative numbers. For example:

-3.45 x 10^(-2)

Q: Can I use scientific notation with decimal points?

A: Yes, you can use scientific notation with decimal points. For example:

3.45 x 10^(-2)

Q: What are some common applications of scientific notation?

A: Some common applications of scientific notation include:

  • Chemistry: Scientific notation is commonly used in chemistry to express the concentration of solutions, the amount of substances, and the results of chemical reactions.
  • Physics: Scientific notation is used in physics to express the results of measurements, the values of physical constants, and the equations of motion.
  • Engineering: Scientific notation is used in engineering to express the results of calculations, the values of physical properties, and the specifications of materials and equipment.
  • Computer Science: Scientific notation is used in computer science to express the results of calculations, the values of variables, and the specifications of algorithms and data structures.

Conclusion

In conclusion, scientific notation and standard notation are two ways of expressing numbers in a more manageable and readable format. By understanding how to express numbers in both scientific and standard notation, we can better understand and work with large and small numbers in a variety of applications.