To convert the repeating decimal \( 0.14\overline{14} \) to a fraction, let's represent it with a variable:
Let \( x = 0.141414...\).
Now, to eliminate the repeating part, we can multiply by 100 (because the repeat cycle is 2 digits):
\[ 100x = 14.141414... \]
Next, we subtract the original \( x \) from this equation to eliminate the repeating decimal:
\[ 100x - x = 14.141414... - 0.141414... \]
This simplifies to:
\[ 99x = 14 \]
Now, solving for \( x \):
\[ x = \frac{14}{99} \]
Thus, \( 0.14\overline{14} = \frac{14}{99} \).
The correct answer among your options is:
1499 Start Fraction 14 over 99 End Fraction