1. Which digit is located at the 2006th place after the decimal point in the decimal representation of the number $\frac{469}{1998} ?$
Solution.

$$
\frac{469}{1998}=469: 1998=0.2347347 \ldots
$$

Note. The use of a calculator is not allowed!

We observe that (after the digit 2 in the first decimal place) the period of three digits 347 repeats.

It repeats 668 times, because

$$
2005=668 \cdot 3+1
$$

The number at the 2006th place is the first digit of the period, the number 3.