The decimal 0.2626262626 is a repeating decimal (0.26 with the "26" repeating). To convert it to a fraction, we can use the following method:
Let \( x = 0.262626...\)
To eliminate the repeating part, we can multiply both sides by 100 (since the repeating block has 2 digits):
\[ 100x = 26.262626... \]
Now we can set up an equation by subtracting the original \( x = 0.262626...\) from this new equation:
\[ 100x - x = 26.262626... - 0.262626... \]
This simplifies to:
\[ 99x = 26 \]
Now, solving for \( x \):
\[ x = \frac{26}{99} \]
So, the decimal 0.2626262626 can be expressed as the fraction \( \frac{26}{99} \).
Thus, the correct answer is:
E. 26/99