Express $3.2\overline{53}$ as a fraction in the form $\dfrac{x}{y}$, where x, y ∈ I and y ≠ 0.

Let x = $3.2\overline{53}$

x = 3.2535353………….. ----------(1)

Multiplying both side with 10, we get

10x = 32.535353………….. ----------(2)

Multiplying both side with 1000 in eqn 1, we get

1000x = 3253.535353………….. ----------(3)

Subtracting equation (2) from equation (3), we get

1000x - 10x = 3253.535353………….. - 32.535353…………..

990x = 3221

x = $\dfrac{3221}{990}$

Hence, $3.2\overline{53} = \dfrac{3221}{990}$.