Answered

Which number is correctly written in scientific notation?


A$2.520 \times 10^3$
B$10 \times 10^3$
C$0.2520 \times 10^{-3}$
D$25.20 \times 10^3$

Verified Answer :

  • Recall that scientific notation requires the form \(a \times 10^n\) where \(1 \leq |a| < 10\).
  • Analyze each coefficient \(a\) to check if it fits the specified range.
  • Determine that only \(2.520 \times 10^3\) meets the requirement as \(1 \leq 2.520 < 10\).
  • Conclude the final answer is \(\boxed{2.520 \times 10^3}\).

Explanation

  1. Understanding Scientific Notation

To identify which number is correctly written in scientific notation, we must recall the definition. A number is expressed in scientific notation if it is in the form \(a \times 10^n\), where \(a\) is a coefficient such that \(1 \leq |a| < 10\), and \(n\) is an integer representing the exponent. We will evaluate each given option against this requirement.

  1. Evaluating the Options

Let's examine each option provided:

  • Option A: \(2.520 \times 10^3\). Here, \(a = 2.520\). Since \(1 \leq 2.520 < 10\), this number satisfies the condition for scientific notation.
  • Option B: \(10 \times 10^3\). Here, \(a = 10\). The condition for scientific notation requires \(|a| < 10\). Since \(10\) is not strictly less than \(10\), this is not in correct scientific notation (it would be written as \(1 \times 10^4\)).
  • Option C: \(0.2520 \times 10^{-3}\). Here, \(a = 0.2520\). The condition for scientific notation requires \(|a| \geq 1\). Since \(0.2520 < 1\), this is not in correct scientific notation (it would be written as \(2.520 \times 10^{-4}\)).
  • Option D: \(25.20 \times 10^3\). Here, \(a = 25.20\). The condition for scientific notation requires \(|a| < 10\). Since \(25.20 > 10\), this is not in correct scientific notation (it would be written as \(2.520 \times 10^4\)).
  1. Conclusion

Based on our analysis, only the first option, \(2.520 \times 10^3\), satisfies the necessary criteria for scientific notation. Therefore, it is the correctly written number. The final answer is \(\boxed{2.520 \times 10^3}\).

Examples

Scientific notation is used in many fields like astronomy and chemistry to express very large or very small numbers compactly. For example, the distance from the Earth to the Sun is approximately \(1.496 \times 10^8\) kilometers. By using this standard format, scientists can perform calculations and compare magnitudes much more easily than by writing out all the zeros. Similarly, the mass of a single atom is extremely small and is often represented in scientific notation, such as \(1.67 \times 10^{-27}\) kilograms.

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