Question

Can someone help me out with this please?

Answer 1

Answer:

$3781/9000$

Step-by-step explanation:

$0.42\overline{1}=42/100+0.00\overline{1}$.

Recall that $0.\overline{1}=1/9$.

So, we want $42/100+1/9*1/1000$.

This simplifies to $21/50+1/9000$.

We know that $21/50=(21*180)/(50*180)=3780/9000$.

So, our expression is $3780/9000+1/9000=3781/9000$, which can't be simplified more.

So, our answer is $\boxed{3781/9000}$ and we're done!