To determine which decimal is equivalent to [tex]\(3 \times 10^{-2}\)[/tex], let's break it down step-by-step.
1. Understanding the Notation:
- The expression [tex]\(3 \times 10^{-2}\)[/tex] is a way to represent a number in scientific notation. Here, [tex]\(3\)[/tex] is the coefficient, and [tex]\(10^{-2}\)[/tex] signifies that we are multiplying by 10 raised to the power of [tex]\(-2\)[/tex].
2. Interpreting [tex]\(10^{-2}\)[/tex]:
- The notation [tex]\(10^{-2}\)[/tex] means 1 divided by [tex]\(10^2\)[/tex]. Specifically, [tex]\(10^2 = 100\)[/tex].
- Therefore, [tex]\(10^{-2} = \frac{1}{100} = 0.01\)[/tex].
3. Multiplying the Coefficient:
- Now, we need to multiply the coefficient 3 by [tex]\(0.01\)[/tex]. Thus,
[tex]\[
3 \times 0.01 = 0.03
\][/tex]
4. Matching the Decimal:
- We need to compare [tex]\(0.03\)[/tex] with the provided options to determine the equivalent decimal number. The options given are:
- (A) 0.03
- (B) 0.003
- (C) 300.0
- (D) 0.006
5. Conclusion:
- After comparing, we see that the correct decimal equivalent of [tex]\(3 \times 10^{-2}\)[/tex] is [tex]\(0.03\)[/tex], which matches option (A).
Thus, the correct answer is:
[tex]\[
\boxed{\text{A}}
\][/tex]
