To convert the repeating decimal \(0.2626262626...\) into a fraction, we can follow these steps:
Let \(x = 0.262626...\).
To eliminate the repeating part, we can multiply by 100 (because the repeating part "26" has two digits):
\[ 100x = 26.262626... \]
Now we have two equations:
- \(x = 0.262626...\)
- \(100x = 26.262626...\)
Next, we subtract the first equation from the second:
\[ 100x - x = 26.262626... - 0.262626... \] \[ 99x = 26 \]
Now, divide both sides by 99:
\[ x = \frac{26}{99} \]
Thus, the repeating decimal \(0.2626262626...\) as a fraction is \(\frac{26}{99}\).
The correct response is:
2699: 26 over 99.