To solve for [tex]\(0.333\)[/tex] written in its simplest fraction form, we begin by expressing it as a fraction.
1. We recognize that [tex]\(0.333\)[/tex] can be written as a ratio of two integers. Specifically, [tex]\(0.333\)[/tex] can initially be expressed as:
[tex]\[
0.333 = \frac{333}{1000}
\][/tex]
This is because [tex]\(0.333\)[/tex] is equivalent to [tex]\( \frac{333}{1000} \)[/tex] when considering the decimal places.
2. Next, we need to simplify the fraction [tex]\( \frac{333}{1000} \)[/tex]. To do this, we find the greatest common divisor (GCD) of the numerator (333) and the denominator (1000).
The GCD of 333 and 1000 is found to be 1. This tells us that the fraction [tex]\( \frac{333}{1000} \)[/tex] is already in its simplest form.
3. Therefore, the simplest form of [tex]\( \frac{333}{1000} \)[/tex] remains:
[tex]\[
\frac{333}{1000}
\][/tex]
Given the options, the correct answer is:
A) [tex]\( \frac{333}{1000} \)[/tex]
