My 9 year old child's method
We must convert b in the denominator to 100. Thus we must multiply numerator and denominator by $100/b$, because we can't change $a/b$. Then $\color{violet}{\dfrac{a}{b}} \equiv \color{violet}{\dfrac{a}{b}} \times \dfrac{\frac{100}{b}}{\frac{100}{b}} \equiv \dfrac{ {\frac ab \times 100}}{100} \equiv \dfrac ab \times \color{limegreen}{100} \times \color{red}{\dfrac1{100}} \equiv \dfrac ab \times \color{limegreen}{100} \color{red}{\%}$.
But why does her answer differ from Mohd Saad's answer?
We're NOT asking about Mohd Saad's method. We both know $\dfrac{a}{b} = \dfrac{n}{100} \iff \dfrac{a}{b} \times 100 = n$, because you simply multiply both sides by 100.
But Mohd Saad's answer final answer is merely $\frac{a}{b} • 100 = n =$ numerator. Who made a mistake, Mohd Saad or my daughter? Why aren't Mohd's and my daughter's answers selfsame?
Your daughter and Mohd Saad are asking related but slightly different questions. Your daughter is asking what is the value of $\frac{a}{b}$ expressed as a percentage. Mohd Saad is saying to express $\frac{a}{b}$ as $n\%$ and asking what $n$ is.
So neither is wrong. When you talk about the "answer" you mean something that equals $\frac{a}{b}$. But Mohd Saad's $n$ does not equal $\frac{a}{b}$; it is $n\%$ that equals $\frac{a}{b}$. So $n\%$ is the answer in your sense of the word "answer".
Mohd Saad, in essence, says $\frac{a}{b}=n\%=\frac{n}{100}$ and solves for $n$. Now $n=100\frac{a}{b}$ and one concludes that $\frac{a}{b}=100\frac{a}{b}\%$, the same as your daughter's answer.