Question 7
The fraction $\frac14$ has this property: appending the digit $6$ to its numerator $n$ times and prefixing that digit to its denominator $n$ times gives $\frac{166\cdots6}{66\cdots64}=\frac14$ for all $n\ge1$. Its numerator and denominator are single digits, the denominator larger. Find all other such fractions; the repeated digit need not be $6$.