Express The Following Quantity In Scientific Notation. The Answer Needs To Have The Correct Number Of Significant Figures.$21,300,000 \text{ ML}$A. $2.1 \times 10^7 \text{ ML}$B. $2.13 \times 10^7 \text{ ML}$C.

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Understanding Scientific Notation

Scientific notation is a way of expressing very large or very small numbers in a more manageable form. It consists of a number between 1 and 10, multiplied by a power of 10. This notation is commonly used in mathematics, physics, and engineering to simplify calculations and express quantities in a more compact form.

Significant Figures

Significant figures are the digits in a measurement that are known to be reliable and certain. They are used to express the precision of a measurement and are an essential concept in scientific notation. When expressing a quantity in scientific notation, the number of significant figures is critical, as it determines the precision of the measurement.

Expressing the Given Quantity in Scientific Notation

The given quantity is 21,300,000 mL21,300,000 \text{ mL}. To express this quantity in scientific notation, we need to convert it to a number between 1 and 10, multiplied by a power of 10.

Step 1: Convert the Number to a Value between 1 and 10

To convert the number 21,300,00021,300,000 to a value between 1 and 10, we can divide it by 10710^7, which is equal to 10,000,000.

21,300,00010,000,000=2.13\frac{21,300,000}{10,000,000} = 2.13

Step 2: Determine the Power of 10

The power of 10 is determined by the number of places we moved the decimal point to the left to get a value between 1 and 10. In this case, we moved the decimal point 7 places to the left, so the power of 10 is 10710^7.

Step 3: Express the Quantity in Scientific Notation

Now that we have the value between 1 and 10 and the power of 10, we can express the quantity in scientific notation.

21,300,000 mL=2.13×107 mL21,300,000 \text{ mL} = 2.13 \times 10^7 \text{ mL}

Analyzing the Options

Let's analyze the options given:

A. $2.1 \times 10^7 \text{ mL}$

This option has only 2 significant figures, which is not sufficient to express the given quantity.

B. $2.13 \times 10^7 \text{ mL}$

This option has 3 significant figures, which is the correct number of significant figures for the given quantity.

C. (Not provided)

Conclusion

In conclusion, the correct answer is B. $2.13 \times 10^7 \text{ mL}$. This option has the correct number of significant figures and expresses the given quantity in scientific notation.

Discussion

Scientific notation is a powerful tool for expressing large or small numbers in a more manageable form. It is essential to understand the concept of significant figures and how to apply it when expressing quantities in scientific notation. By following the steps outlined above, we can express any quantity in scientific notation and determine the correct number of significant figures.

Common Mistakes

When expressing quantities in scientific notation, it is common to make mistakes related to significant figures. Some common mistakes include:

  • Not having enough significant figures
  • Having too many significant figures
  • Not understanding the concept of significant figures

Tips and Tricks

To avoid common mistakes and ensure accurate results, follow these tips and tricks:

  • Always check the number of significant figures
  • Use the correct power of 10
  • Understand the concept of significant figures

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 consists of a number between 1 and 10, multiplied by a power of 10.

Q: Why is scientific notation important?

A: Scientific notation is important because it allows us to express large or small numbers in a more compact form, making it easier to perform calculations and understand complex concepts.

Q: How do I express a number in scientific notation?

A: To express a number in scientific notation, follow these steps:

  1. Convert the number to a value between 1 and 10.
  2. Determine the power of 10 by counting the number of places you moved the decimal point to the left.
  3. Express the number in scientific notation by multiplying the value between 1 and 10 by the power of 10.

Q: What is the correct number of significant figures in scientific notation?

A: The correct number of significant figures in scientific notation is determined by the number of digits in the value between 1 and 10. For example, if the value is 2.13, the correct number of significant figures is 3.

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

A: To determine the correct power of 10 in scientific notation, count the number of places you moved the decimal point to the left to get a value between 1 and 10.

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

A: Scientific notation and exponential notation are similar, but they have some key differences. Scientific notation is used to express numbers in a more compact form, while exponential notation is used to express numbers as powers of a base.

Q: Can I use scientific notation with negative numbers?

A: Yes, you can use scientific notation with negative numbers. To do this, simply multiply the value between 1 and 10 by the power of 10, and then add a negative sign to the 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 value between 1 and 10 by the power of 10.
  2. Add the decimal point to the value between 1 and 10, and then move it to the right by the number of places indicated by the power of 10.

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

A: Some common mistakes to avoid when using scientific notation include:

  • Not having enough significant figures
  • Having too many significant figures
  • Not understanding the concept of significant figures
  • Not using the correct power of 10

Q: How do I use scientific notation in real-world applications?

A: Scientific notation is used in a wide range of real-world applications, including:

  • Physics and engineering
  • Chemistry and biology
  • Mathematics and statistics
  • Computer science and programming

By understanding the basics of scientific notation and how to apply it in different contexts, you can use it to solve complex problems and express numbers in a more compact and manageable form.