Answer:
[tex]3781/9000[/tex]
Step-by-step explanation:
[tex]0.42\overline{1}=42/100+0.00\overline{1}[/tex].
Recall that [tex]0.\overline{1}=1/9[/tex].
So, we want [tex]42/100+1/9*1/1000[/tex].
This simplifies to [tex]21/50+1/9000[/tex].
We know that [tex]21/50=(21*180)/(50*180)=3780/9000[/tex].
So, our expression is [tex]3780/9000+1/9000=3781/9000[/tex], which can't be simplified more.
So, our answer is [tex]\boxed{3781/9000}[/tex] and we're done!
