Express $4.\overline{054}$ as a common fraction in lowest terms.
I notice that this is a repeating decimal, so I can use a technique where I multiply both sides of an equation by a power of 10 to shift the decimal point and then subtract to eliminate the repeating part. First, I let $x = 4.\overline{054}$. Then, I multiply both sides by 1000, since there are three digits in the repeating part. This gives me $1000x = 4054.\overline{054}$. Next, I subtract $x$ from both sides, which gives me $999x = 4050$. I can simplify this equation by dividing both sides by 3, since both numbers are multiples of 3. This gives me $333x = 1350$. Now, I can solve for $x$ by dividing both sides by 333, which gives me $x = \frac{1350}{333}$. I can reduce this fraction by dividing both the numerator and the denominator by 9, since both numbers are multiples of 9. This gives me $x = \frac{150}{37}$, which is the final answer. 