109. From the digits $1,2,3,4$, all possible positive decimal fractions with one, two, or three decimal places are formed, each containing each of these digits exactly once. Find the sum of these fractions.
Solution. From the digits $1,2,3,4$, 24 different integers can be formed $(4 \cdot 3 \cdot 2=24)$; in these numbers, each of the given digits appears 6 times in each place value $(24: 4=6)$. Therefore, the sum of the digits in each place value is $60((1+2+3+4) \cdot 6=60)$. Consequently, the sum of all these 24 numbers is

$$
60+600+6000+60000=66660 .
$$

From this, it is clear that the desired sum is

$$
6666+666.6+66.66=7399.26
$$

Answer: 7399.26 .