Select All The Correct Answers.Jim Writes Down A Large Number. The Number Is 543 Followed By 12 Zeroes. How Would Jim Express This Number?A. $5.43 \times 10^{14}$ B. $5.43 \times 10^{-12}$ C. 5.43 E 14 D. $5.43 \times

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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 involves expressing a number as a product of a number between 1 and 10 and a power of 10. This notation is commonly used in mathematics, physics, and engineering to simplify complex calculations.

Expressing the Number 543 Followed by 12 Zeroes

Jim writes down a large number, 543 followed by 12 zeroes. To express this number in scientific notation, we need to determine the power of 10 that would result in 12 zeroes. Since each zero represents a power of 10, we can calculate the power of 10 as follows:

12 zeroes = 10^12

However, we need to express the number 543 in the correct format. Since the number is followed by 12 zeroes, we can express it as:

543 × 10^12

Converting to Scientific Notation

To convert the number to scientific notation, we need to express it as a product of a number between 1 and 10 and a power of 10. In this case, we can express the number as:

5.43 × 10^14

This is because 543 is equal to 5.43 × 100, and 100 is equal to 10^2. Therefore, we can rewrite the number as:

5.43 × 10^2 × 10^12

Combining the powers of 10, we get:

5.43 × 10^14

Evaluating the Answer Choices

Now that we have expressed the number in scientific notation, let's evaluate the answer choices:

A. 5.43×10145.43 \times 10^{14}

This is the correct answer.

B. 5.43×10−125.43 \times 10^{-12}

This is incorrect because the power of 10 is negative, which would result in a very small number.

C. 5.43 E 14

This is incorrect because the notation "E" is not commonly used in scientific notation. The correct notation is "× 10^".

D. 5.43×10125.43 \times 10^{12}

This is incorrect because the power of 10 is not correct. We need to add 2 to the power of 10 to get the correct result.

Conclusion

In conclusion, Jim can express the number 543 followed by 12 zeroes as 5.43×10145.43 \times 10^{14}. This is the correct answer choice. Scientific notation is a powerful tool for expressing large numbers in a more manageable form, and it is commonly used in mathematics, physics, and engineering.

Key Takeaways

  • Scientific notation is a way of expressing very large or very small numbers in a more manageable form.
  • To express a number in scientific notation, we need to determine the power of 10 that would result in the correct number of zeroes.
  • The power of 10 is calculated by counting the number of zeroes.
  • The number should be expressed as a product of a number between 1 and 10 and a power of 10.
  • The correct notation is "× 10^", not "E".

Practice Problems

  1. Express the number 2,456,789,012,345 in scientific notation.
  2. Express the number 0.000000000000123 in scientific notation.
  3. Express the number 1,234,567,890,123 in scientific notation.

Solutions

  1. 2.456789012345×10122.456789012345 \times 10^{12}
  2. 1.23×10−131.23 \times 10^{-13}
  3. 1.234567890123×10121.234567890123 \times 10^{12}
    Scientific Notation Q&A ==========================

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 involves expressing a number as a product of a number between 1 and 10 and a power of 10.

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

A: To express a number in scientific notation, you need to determine the power of 10 that would result in the correct number of zeroes. The power of 10 is calculated by counting the number of zeroes. The number should be expressed as a product of a number between 1 and 10 and a power of 10.

Q: What is the correct notation for scientific notation?

A: The correct notation for scientific notation is "× 10^", not "E". For example, the number 543 followed by 12 zeroes can be expressed as 5.43×10145.43 \times 10^{14}.

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

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

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

A: Scientific notation and exponential notation are similar, but they are not the same thing. Exponential notation involves expressing a number as a product of a number and a power of a base other than 10, such as 2 or 10. Scientific notation, on the other hand, involves expressing a number as a product of a number between 1 and 10 and a power of 10.

Q: When should I use scientific notation?

A: You should use scientific notation when you need to express very large or very small numbers in a more manageable form. This is particularly useful in mathematics, physics, and engineering, where large numbers are common.

Q: How do I evaluate expressions in scientific notation?

A: To evaluate expressions in scientific notation, you need to follow the order of operations (PEMDAS). This means that you need to evaluate any expressions inside parentheses first, followed by any exponential expressions, and then any multiplication and division expressions.

Q: Can I use scientific notation with negative numbers?

A: Yes, you can use scientific notation with negative numbers. To do this, you need to express the negative number as a product of a negative number between 1 and 10 and a power of 10.

Q: Can I use scientific notation with fractions?

A: Yes, you can use scientific notation with fractions. To do this, you need to express the fraction as a product of a number between 1 and 10 and a power of 10.

Q: How do I convert between scientific notation and standard notation?

A: To convert between scientific notation and standard notation, you need to move the decimal point to the left or right by the number of places indicated by the power of 10. For example, the number 5.43×10145.43 \times 10^{14} can be converted to standard notation by moving the decimal point 14 places to the right.

Q: What are some common applications of scientific notation?

A: Scientific notation has many common applications in mathematics, physics, and engineering. Some examples include:

  • Expressing large numbers in a more manageable form
  • Simplifying complex calculations
  • Expressing small numbers in a more manageable form
  • Converting between different units of measurement

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

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

  • Using the wrong power of 10
  • Expressing a number as a product of a number and a power of a base other than 10
  • Failing to follow the order of operations (PEMDAS)
  • Using scientific notation with negative numbers or fractions incorrectly