A student prepares a stock solution of a strong base by dissolving
\(\text{NaOH(s)}\) in water to obtain a \(0.10\text{ M }\text{NaOH(aq)}\) solution. The student then performs two successive tenfold serial dilutions: first, a \(10.0\text{ mL}\) sample of the stock solution is diluted with distilled water to a total volume of \(100.0\text{ mL}\), and then a \(10.0\text{ mL}\) sample of that resulting solution is diluted with distilled water to a total volume of \(100.0\text{ mL}\). What is the \(\text{pH}\) of the final diluted solution at \(25\,^\circ\text{C}\)?