To express \(0.0000000003\) seconds in the form of \(a \times 10^n\) where \(1 < a < 10\), we start by rewriting the number in scientific notation.
The number \(0.0000000003\) can also be written as:
\[ 3 \times 10^{-10} \]
However, this does not fit the requirement of \(1 < a < 10\) because \(3 < 10\) but we have an exponent of \(-10\) which does not match the options given.
From the list of options:
A. \(3 \times 10^9\)
B. \(3 \times 10^{-8}\)
C. \(3 \times 10^{-9}\)
D. \(3 \times 10^8\)
The closest representation that fits the criteria provided in the options would be \(3 \times 10^{-9}\) because \(3\) is between 1 and 10, and the exponent \(-9\) provides a value that is equivalent to \(0.000000003\), which means this would still not represent \(0.0000000003\).
Out of the available options, the correct representation of \(0.0000000003\) in a valid scientific notation context based on the choices would actually be:
None of the provided options fit perfectly with the value \(0.0000000003\) correctly.
The correct answer, without the choices, should be \(3 \times 10^{-10}\), but from the listed options, \(C. 3 \times 10^{-9}\) is the only one that fits the \(1 < a < 10\) condition visually.
Hence, the corrected representation contextially based on the options available, I would choose:
C. \(3 \times 10^{-9}\).
(Note: It should be noted that this value does not correctly reflect \(0.0000000003\) but seems to be the closest option given the constraints.)
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