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Chapter 7: Problem 27

Convert each number into scientific notation. $$9727.3$$

Short Answer

Expert verified
9727.3 in scientific notation is \(9.7273 \times 10^3\).

Step by step solution

01

- Identify the initial part

Find the initial part of the given number 9727.3 that will be between 1 and 10. For 9727.3, it's 9.7273 because moving the decimal place 3 positions to the left results in 9.7273.
02

- Determine the exponent

Count the number of places the decimal point needs to move to go from the original number to the value between 1 and 10. For 9727.3, the decimal moves 3 places to the left, so the exponent is 3.
03

- Write in scientific notation

Combine the initial part and the exponent into the scientific notation format. Therefore, 9727.3 in scientific notation is \(9.7273 \times 10^3\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Decimal Places
Decimal places indicate the position of numbers to the right of the decimal point. Understanding decimal places is essential for scientific notation.

When converting a number to scientific notation, you often deal with shifting the decimal point. This is to transform the number into a form where it falls between 1 and 10.

For example, with the number 9727.3, you move the decimal point three places to the left. This results in 9.7273, where we have kept the same number of decimal places as in the original number.

Maintaining the same decimal places helps retain the accuracy of the original number after the conversion.
Exponent
An exponent in scientific notation indicates how many places the decimal point has moved. It's written as a power of 10.

In the number 9727.3, the decimal point is shifted three places to the left to get 9.7273. This movement to the left is represented by a positive exponent. So, the exponent is 3, and the number in scientific notation is written as \(9.7273 \times 10^3\).

The exponent tells you that 9.7273 should be multiplied by 10 three times, effectively moving the decimal point back to its original position in 9727.3.
Number Conversion
Converting a regular number to scientific notation involves changing the format without altering its value.

The key steps are:
  • Identify the initial part: This is the number between 1 and 10. For 9727.3, moving the decimal gives you 9.7273.

  • Determine the exponent: Count how many places you shifted the decimal point. In this case, it's 3 places to the left, giving you an exponent of 3.

  • Write in scientific notation: Combine them, resulting in \(9.7273 \times 10^3\).

This format makes it easier to handle very large or very small numbers efficiently while preserving their value and significance.

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Most popular questions from this chapter

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