Let \( x = 0.989898...\), where the digits "98" repeat indefinitely.
To eliminate the repeating decimal, we can multiply \( x \) by 100 (which shifts the decimal point two places to the right):
\[ 100x = 98.989898... \]
Now, we can set up a system of equations using these two equations:
- \( x = 0.989898...\)
- \( 100x = 98.989898...\)
Next, we'll subtract the first equation from the second:
\[ 100x - x = 98.989898... - 0.989898... \]
This simplifies to:
\[ 99x = 98 \]
Now, we solve for \( x \):
\[ x = \frac{98}{99} \]
The fraction \(\frac{98}{99}\) is already in its simplest form, as 98 and 99 have no common factors other than 1.
Thus, the repeating decimal \(0.989898...\) can be expressed as the fraction
\[ \boxed{\frac{98}{99}}. \]