Answer
a)
The rational number named by $0.27272727\cdots$ is $\dfrac{3}{11}$.
b)
The rational number named by $0.90909090\cdots$ is $\dfrac{10}{11}$.
Work Step by Step
a)
We have given $0.18181818\cdots=\dfrac{2}{11}$ and $0.09090909\cdots=\dfrac{1}{11}$.
Adding the two equations will give $0.27272727\cdots=\dfrac{2}{11}+\dfrac{1}{11}=\dfrac{3}{11}$
b)
We have given $0.09090909\cdots=\dfrac{1}{11}$.
Multiply the equation by $10$.
We get, $0.90909090\cdots=\dfrac{10}{11}$
