To convert \(0.14\overline{14}\) to a fraction, we can denote it as \(x = 0.141414...\). Then, we multiply by 100 to shift the decimal point:
\(100x = 14.141414...\)
Next, subtract the original \(x\) from this equation:
\(100x - x = 14.141414... - 0.141414...\)
This simplifies to:
\(99x = 14\)
Now, divide both sides by 99:
\(x = \frac{14}{99}\)
So, \(0.14\overline{14} = \frac{14}{99}\).