Question 5
When a student multiplied the number $66$ by the repeating decimal $$
1.\overline{ab} = 1.ababab\ldots,
$$ where $a$ and $b$ are digits, he did not notice the notation and just multiplied $66$ by the terminating decimal $1.ab.$ Later he found that his answer was $0.5$ less than the correct answer.
What is the two-digit integer $\overline{ab}?$
1.\overline{ab} = 1.ababab\ldots,
$$ where $a$ and $b$ are digits, he did not notice the notation and just multiplied $66$ by the terminating decimal $1.ab.$ Later he found that his answer was $0.5$ less than the correct answer.
What is the two-digit integer $\overline{ab}?$