Express Your Answer In Scientific Notation.$4.9 \cdot 10^4 - 8200 = \square$

Feb 27, 2025 by ADMIN 77 views

**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. This notation is commonly used in mathematics and science to simplify calculations and express very large or very small numbers in a more manageable form.

Understanding the Problem

The given problem is to express the result of the subtraction of 8200 from 4.9 multiplied by 10 to the power of 4 in scientific notation. To solve this problem, we need to first perform the multiplication and then subtract 8200 from the result.

Step 1: Multiply 4.9 by 10 to the Power of 4

To multiply 4.9 by 10 to the power of 4, we need to multiply 4.9 by 10,000. This can be done by moving the decimal point in 4.9 four places to the right, resulting in 49,000.

Step 2: Subtract 8200 from the Result

Now that we have the result of the multiplication, we need to subtract 8200 from it. To do this, we can simply subtract 8200 from 49,000, resulting in 40,800.

Expressing the Result in Scientific Notation

Now that we have the result of the subtraction, we need to express it in scientific notation. To do this, we need to move the decimal point in 40,800 to the left until we have a number between 1 and 10. This can be done by moving the decimal point three places to the left, resulting in 4.08.

The Final Answer

The final answer is 4.08 x 10^4.

Why Scientific Notation is Important

Scientific notation is an important concept in mathematics and science because it allows us to express very large or very small numbers in a more manageable form. This notation is commonly used in calculations involving very large or very small numbers, such as those encountered in physics, chemistry, and engineering.

Examples of Scientific Notation

Scientific notation is used in a variety of fields, including:

Physics: Scientific notation is used to express the speed of light, the distance between galaxies, and other very large or very small quantities.
Chemistry: Scientific notation is used to express the concentration of solutions, the amount of substance in a sample, and other quantities that are often very large or very small.
Engineering: Scientific notation is used to express the size of structures, the amount of material used in construction, and other quantities that are often very large or very small.

Conclusion

In conclusion, scientific notation is an important concept in mathematics and science that allows us to express very large or very small numbers in a more manageable form. By understanding how to express numbers in scientific notation, we can simplify calculations and express quantities in a more meaningful way.

Common Mistakes to Avoid

When working with scientific notation, there are several common mistakes to avoid:

Incorrect placement of the decimal point: When moving the decimal point in a number to express it in scientific notation, it is easy to make mistakes. To avoid this, make sure to move the decimal point the correct number of places.
Incorrect exponent: When expressing a number in scientific notation, the exponent must be correct. To avoid this, make sure to use the correct exponent.
Incorrect calculation: When performing calculations involving scientific notation, it is easy to make mistakes. To avoid this, make sure to follow the order of operations and use the correct mathematical operations.

Tips for Working with Scientific Notation

When working with scientific notation, here are some tips to keep in mind:

Use a calculator: When working with very large or very small numbers, it is often helpful to use a calculator to simplify calculations.
Use a spreadsheet: When working with large datasets, it is often helpful to use a spreadsheet to organize and analyze the data.
Check your work: When working with scientific notation, it is always a good idea to check your work to make sure that you have made no mistakes.

Real-World Applications of Scientific Notation

Scientific notation has many real-world applications, including:

Astronomy: Scientific notation is used to express the distance between stars, the size of galaxies, and other very large or very small quantities.
Medicine: Scientific notation is used to express the concentration of medications, the amount of substance in a sample, and other quantities that are often very large or very small.
Computer Science: Scientific notation is used to express the size of data structures, the amount of memory used in a program, and other quantities that are often very large or very small.

Conclusion

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 simplify calculations and express very large or very small numbers in a more manageable form.

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

A: To express a number in scientific notation, you need to move the decimal point in the number until you have a number between 1 and 10. Then, you need to multiply the number by 10 raised to the power of the number of places you moved the decimal point.

Q: What is the exponent in scientific notation?

A: The exponent in scientific notation is the power of 10 that you multiply the number by. It is usually written as a small number to the right of the number, such as 10^3 or 10^-2.

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

A: When adding or subtracting numbers in scientific notation, you need to make sure that the exponents are the same. If the exponents are different, you need to convert the numbers to have the same exponent before you can add or subtract them.

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

A: When multiplying or dividing numbers in scientific notation, you can simply multiply or divide the numbers and add or subtract the exponents.

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:

Incorrect placement of the decimal point: When moving the decimal point in a number to express it in scientific notation, it is easy to make mistakes. To avoid this, make sure to move the decimal point the correct number of places.
Incorrect exponent: When expressing a number in scientific notation, the exponent must be correct. To avoid this, make sure to use the correct exponent.
Incorrect calculation: When performing calculations involving scientific notation, it is easy to make mistakes. To avoid this, make sure to follow the order of operations and use the correct mathematical operations.

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

A: Scientific notation has many real-world applications, including:

Astronomy: Scientific notation is used to express the distance between stars, the size of galaxies, and other very large or very small quantities.
Medicine: Scientific notation is used to express the concentration of medications, the amount of substance in a sample, and other quantities that are often very large or very small.
Computer Science: Scientific notation is used to express the size of data structures, the amount of memory used in a program, and other quantities that are often very large or very small.

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

A: To convert a number from scientific notation to standard notation, you need to multiply the number by 10 raised to the power of the exponent. For example, if you have the number 3.4 x 10^2, you would multiply 3.4 by 100 to get 340.

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

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

Q: What are some tips for working with scientific notation?

A: Some tips for working with scientific notation include:

Use a calculator: When working with very large or very small numbers, it is often helpful to use a calculator to simplify calculations.
Use a spreadsheet: When working with large datasets, it is often helpful to use a spreadsheet to organize and analyze the data.
Check your work: When working with scientific notation, it is always a good idea to check your work to make sure that you have made no mistakes.