Express $4.\overline{054}$ as a common fraction in lowest terms.

If we expand it out, we get 4.054054054.....

 

Setting this equal to x, we have:

 

1000x = 4054.054054054...

x = 4.054054054...

 

Subtracting the equations, we get:

 

999x = 4050

 

x = 4050/999

 

x = 450/111

 

x = 150/37