To find the fractional form of the repeating decimal [tex]\(0.\overline{02}\)[/tex], let's denote this repeating decimal by [tex]\(x\)[/tex].
[tex]\[x = 0.02020202\ldots\][/tex]
If we multiply both sides of this equation by 100 (since the repeating segment consists of 2 digits), we get:
[tex]\[100x = 2.02020202\ldots\][/tex]
Next, we subtract the original [tex]\(x\)[/tex] from this new equation:
[tex]\[100x - x = 2.02020202\ldots - 0.02020202\ldots\][/tex]
Simplifying, we have:
[tex]\[99x = 2\][/tex]
Now, we solve for [tex]\(x\)[/tex] by dividing both sides of the equation by 99:
[tex]\[x = \frac{2}{99}\][/tex]
Thus, the repeating decimal [tex]\(0.\overline{02}\)[/tex] is represented as the fraction [tex]\(\frac{2}{99}\)[/tex].
Therefore, the correct answer is:
A. [tex]\(\frac{2}{99}\)[/tex]
