Answer :

Clearly,

1.1011001110001… < 2 < 2.1011001110001…

As, 2 is a rational number.

Therefore, 2 is a required rational number.

Now, We have to find a non-terminating and non-recurring number between 1.1011001110001… and 2.1011001110001…

And one of the possible answer is

1.20200200020000…

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