Use The Calculator To Find The Product Of 4.17 And 2.3 × 10 6 2.3 \times 10^6 2.3 × 1 0 6 . Which Statements Are True About Finding The Product? Check All That Apply.- 4.17 Is Equivalent To 4.17 × 10 6 4.17 \times 10^6 4.17 × 1 0 6 .- 4.17 Is Equivalent To $4.17 \times

by ADMIN 270 views

Understanding Scientific Notation and Multiplication

Scientific notation is a way of expressing very large or very small numbers in a compact form. It consists of a number between 1 and 10, multiplied by a power of 10. In the given problem, we are asked to find the product of 4.17 and 2.3×1062.3 \times 10^6. To do this, we need to understand the rules of multiplication in scientific notation.

Multiplication Rules in Scientific Notation

When multiplying numbers in scientific notation, we follow these rules:

  • We multiply the numbers as if they were in standard form.
  • We add the exponents of the powers of 10.

Let's apply these rules to the given problem.

Finding the Product

To find the product of 4.17 and 2.3×1062.3 \times 10^6, we first multiply the numbers as if they were in standard form:

4.17 × 2.3 = 9.591

Next, we add the exponents of the powers of 10:

10610^6 × 10010^0 = 106+010^{6+0} = 10610^6

So, the product of 4.17 and 2.3×1062.3 \times 10^6 is 9.591×1069.591 \times 10^6.

Evaluating the Statements

Now, let's evaluate the given statements:

  • 4.17 is equivalent to 4.17×1064.17 \times 10^6: This statement is false. 4.17 is equivalent to 4.17×1004.17 \times 10^0, not 4.17×1064.17 \times 10^6.
  • 4.17 is equivalent to 4.17×1004.17 \times 10^0: This statement is true. 4.17 can be written as 4.17×1004.17 \times 10^0.
  • 4.17 is equivalent to 4.17×10−64.17 \times 10^{-6}: This statement is false. 4.17 is equivalent to 4.17×1004.17 \times 10^0, not 4.17×10−64.17 \times 10^{-6}.

In conclusion, the product of 4.17 and 2.3×1062.3 \times 10^6 is 9.591×1069.591 \times 10^6. We also found that 4.17 is equivalent to 4.17×1004.17 \times 10^0, not 4.17×1064.17 \times 10^6 or 4.17×10−64.17 \times 10^{-6}.

Key Takeaways

  • When multiplying numbers in scientific notation, we follow the rules of multiplication in standard form and add the exponents of the powers of 10.
  • 4.17 is equivalent to 4.17×1004.17 \times 10^0, not 4.17×1064.17 \times 10^6 or 4.17×10−64.17 \times 10^{-6}.

Conclusion

In this article, we used the calculator to find the product of 4.17 and 2.3×1062.3 \times 10^6. We also evaluated the given statements and found that 4.17 is equivalent to 4.17×1004.17 \times 10^0, not 4.17×1064.17 \times 10^6 or 4.17×10−64.17 \times 10^{-6}. We hope this article has helped you understand the rules of multiplication in scientific notation and how to apply them in real-world problems.
Scientific Notation Q&A

In this article, we will answer some frequently asked questions about scientific notation and multiplication.

Q: What is scientific notation?

A: Scientific notation is a way of expressing very large or very small numbers in a compact form. It consists of a number between 1 and 10, multiplied by a power of 10.

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

A: To write a number in scientific notation, you need to express it as a number between 1 and 10, multiplied by a power of 10. For example, the number 456,000 can be written as 4.56×1054.56 \times 10^5.

Q: How do I multiply numbers in scientific notation?

A: When multiplying numbers in scientific notation, you follow these rules:

  • Multiply the numbers as if they were in standard form.
  • Add the exponents of the powers of 10.

Q: Can you give an example of multiplying numbers in scientific notation?

A: Let's say we want to multiply 2.3×1062.3 \times 10^6 and 4.17×1004.17 \times 10^0. First, we multiply the numbers as if they were in standard form:

2.3 × 4.17 = 9.591

Next, we add the exponents of the powers of 10:

10610^6 × 10010^0 = 106+010^{6+0} = 10610^6

So, the product of 2.3×1062.3 \times 10^6 and 4.17×1004.17 \times 10^0 is 9.591×1069.591 \times 10^6.

Q: What is the difference between 4.17×1064.17 \times 10^6 and 4.17×1004.17 \times 10^0?

A: 4.17×1064.17 \times 10^6 is a number in scientific notation, where 4.17 is multiplied by 10610^6. On the other hand, 4.17×1004.17 \times 10^0 is also a number in scientific notation, where 4.17 is multiplied by 10010^0. The key difference is that 4.17×1064.17 \times 10^6 is a much larger number than 4.17×1004.17 \times 10^0.

Q: Can you give an example of a real-world application of scientific notation?

A: Scientific notation is commonly used in physics and engineering to express large or small numbers. For example, the speed of light is approximately 3.00×1083.00 \times 10^8 meters per second. This is a much more compact and easier-to-read way of expressing the speed of light than writing it out in standard form.

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

A: To convert a number from scientific notation to standard form, you need to multiply the number by the power of 10. For example, to convert 4.56×1054.56 \times 10^5 to standard form, you would multiply 4.56 by 10510^5, which is equal to 456,000.

Q: Can you give an example of converting a number from scientific notation to standard form?

A: Let's say we want to convert 2.3×1062.3 \times 10^6 to standard form. To do this, we multiply 2.3 by 10610^6, which is equal to 2,300,000.

Conclusion

In this article, we answered some frequently asked questions about scientific notation and multiplication. We hope this article has helped you understand the basics of scientific notation and how to apply it in real-world problems.