Telangana TET Paper 1 Exam Model Paper 1

Concept:To convert a repeating decimal to a fraction, multiply by a power of 10 to shift the repeating part, then subtract to eliminate repetition.Explanation:Let $x = 0.7\overline{12} = 0.7121212\ldots$The repeating block "12" has two digits, so multiply by 100:$100x = 71.2121212\ldots$Subtract the original $x$:$100x - x = 71.2121212\ldots - 0.7121212\ldots$This gives $99x = 70.5$Convert $70.5$ to a fraction: $70.5 = \frac{141}{2}$So $x = \frac{141}{2} \div 99 = \frac{141}{2} \times \frac{1}{99} = \frac{141}{198}$Simplify by dividing numerator and denominator by $3$:$x = \frac{47}{66}$Answer:$\frac{47}{66}$, which is option A.