To express the number [tex]\(0.009402\)[/tex] in scientific notation, we need to rewrite it in the form [tex]\(a \times 10^b\)[/tex], where [tex]\(1 \leq a < 10\)[/tex] and [tex]\(b\)[/tex] is an integer.
1. Identify the decimal point move:
The given number is [tex]\(0.009402\)[/tex]. To convert this into the form [tex]\(a \times 10^b\)[/tex], we need to move the decimal point such that [tex]\(a\)[/tex] is a number between 1 and 10.
Moving the decimal point three places to the right, we get:
[tex]\[
0.009402 \rightarrow 9.402
\][/tex]
2. Determine the exponent:
Since we moved the decimal point three places to the right, this corresponds to multiplying by [tex]\(10^{-3}\)[/tex]. This is because moving to the right means the exponent is negative.
3. Write in scientific notation:
Hence, [tex]\(0.009402\)[/tex] can be written as:
[tex]\[
0.009402 = 9.402 \times 10^{-3}
\][/tex]
Now, let's match this with the given answer choices:
A. [tex]\(9.402 \times 10^{-6}\)[/tex] — Incorrect exponent.
B. [tex]\(9402 \times 10^6\)[/tex] — Incorrect form and exponent.
C. [tex]\(9.402 \times 10^{-3}\)[/tex] — Correct.
D. [tex]\(9.402 \times 10^3\)[/tex] — Incorrect exponent.
The correct answer is:
[tex]\[
\boxed{C}
\][/tex]
