When a student multiplied the number $66$ by the repeating decimal,  
$\underline{1}.\underline{a} \ \underline{b} \ \underline{a}  \underline{b}\cdots=\underline{1}.\overline{\underline{a} \ \underline{b}},$  
where $a$ and $b$ are digits, he did not notice the notation and just multiplied $66~ times$ $\underline{1}.\underline{a} \ \underline{b}.$ Later he found that his answer is $0.5$ less than the correct answer. Find the $2$-digit number $\underline{a} \ \underline{b}.$

Let's think step by step and output the final answer within \boxed{}.
user