Decimals

Let \(x = 0.43 \overline{54}\)

 

This means that \(100x = 43.\overline{54}\) and \(10,000x = 4354.\overline{54}\)

 

Subtracting the 2 gives us \(9900x = 4311\), meaning \(x = {4311 \over 9900} = \color{brown}\boxed{479 \over1100}\)