Let's write down the natural numbers after the decimal point in sequence:

$$
0,123456789101112 \ldots
$$

Determine the ten-thousandth digit of this decimal.
In the decimal number system, there are 9 single-digit, 90 two-digit, 900 three-digit, 9000 four-digit... natural numbers. Up to the four-digit numbers, this amounts to $9 \cdot 1 + 90 \cdot 2 + 900 \cdot 3 + 9000 \cdot 4 = 38889$ digits. The $40000 - 38889 = 1111$ digits form 222 five-digit numbers, with one digit remaining. Therefore, the fortieth thousandth digit is the first digit of the two hundred and twenty-third five-digit number, which is 10222, and thus it is 1.

Lackner Györgyi (Bp. V., 1. sz. textilip. techn. II. o. t.)