counting numbers finished on 4

Question

What about this problem.

We consider all the numbers ending by 4, concatenated in one super number. What would be its $290_{th}$ digit ?

Could you explain your answer ?

Thanks!

Answer 1

From $4$ to $94$ we have $1+2\cdot9=19$ digits.

From $104$ to $194$ we have $3\cdot10=30$ digits.

From $204$ to $294$ we have $3\cdot10=30$ digits.

From $304$ to $394$ we have $3\cdot10=30$ digits.

...

From $904$ to $994$ we have $3\cdot10=30$ digits.

Altogether we have $19+30\cdot9=289$ digits.

So the digit in the $290$th place is the first digit of $1004$, i.e., $1$.