1. **Problem:** Find the simplest fractional form of the repeating decimal $0.272727...$. 2. **Formula and Explanation:** A repeating decimal $0.ar{ab}$ where $ab$ is a two-digit repeating block can be converted to a fraction by using the formula: $$\text{Fraction} = \frac{\text{repeating digits}}{99}$$ because $99 = 10^2 - 1$ for two repeating digits. 3. **Step-by-step solution:** - The repeating block is $27$. - So, the fraction is: $$\frac{27}{99}$$ - Simplify the fraction by dividing numerator and denominator by their greatest common divisor (GCD), which is $9$: $$\frac{\cancel{27}^3}{\cancel{99}^11}$$ - Thus, the simplest form is: $$\frac{3}{11}$$ 4. **Answer:** The simplest form of $0.272727...$ is $\boxed{\frac{3}{11}}$. The other questions are not solved as per instructions.