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Chapter 10: Problem 609

Convert each number to decimal form. $$9.413 \times 10^{-5}$$

Short Answer

Expert verified
0.00009413

Step by step solution

01

- Identify the Power of 10

Observe that the number is in scientific notation: 9.413 脳 10^{-5}. This means the decimal point needs to be moved 5 places to the left.
02

- Moving the Decimal Point

Start with the number 9.413. To convert it to decimal form, move the decimal point 5 places to the left. Since the exponent is negative (-5), move left:First move: 0.9413Second move: 0.09413Third move: 0.009413Fourth move: 0.0009413Fifth move: 0.00009413
03

- Write the Final Decimal Form

After moving the decimal point five places to the left, the number 9.413 脳 10^{-5} converts to 0.00009413.

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Key Concepts

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

Decimal Form
Understanding decimal form is crucial when working with numbers in various scientific, mathematical, and everyday contexts. Decimal form essentially strips away the scientific notation and expresses the number in a format that is more familiar to most people. For instance, 9.413 脳 10^{-5} is a number in scientific notation but converting it to decimal form gives you a clearer perspective. In decimal form, this number is written as 0.00009413. The process involves shifting the decimal point to make the number comprehendible without any power of 10.
Power of 10
The power of 10 plays a critical role in scientific notation. It indicates how many places you must move the decimal point to convert the number to or from its decimal form. Consider the scientific notation 9.413 脳 10^{-5}: the exponent here is -5. This negative exponent signals that the decimal point needs to be moved 5 places to the left. Conversely, a positive exponent would mean moving the decimal point to the right. Recognizing the power of 10 can simplify complex numbers and make conversions straightforward.
Moving the Decimal Point
Moving the decimal point is a key step in converting scientific notation to decimal form. Let's break it down:
  • Start with the given number in scientific notation, for example, 9.413 脳 10^{-5}.
  • The exponent (-5) tells you to move the decimal point 5 places to the left.
  • Begin with the decimal point right after 9.413.
  • Progress one place at a time to the left:
  • First move: 0.9413
  • Second move: 0.09413
  • Third move: 0.009413
  • Fourth move: 0.0009413
  • Fifth move: 0.00009413
The final step involves writing out the number in its new decimal form: 0.00009413. This simple technique allows for accurate and effective conversion from scientific notation.

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