15. (15 points) Definition: $[a]$ represents the greatest natural number not exceeding $a$, for example $[0.6]=0,[1.25]=1$. If $[5 a-0.9]$ $=3 a+0.7$, then the value of $a$ is.
【Solution】Solution:
$$
\begin{array}{l}
3 a+0.7 \leqslant 5 a-0.9 \leqslant 3 a+1.7 \\
3 a+1.6 \leqslant 5 a \leqslant 3 a+2.6 \\
1.6 \leqslant 2 a \leqslant 2.6 \\
0.8 \leqslant a \leqslant 1.3 \\
\therefore 2.4 \leqslant 3 a \leqslant 3.9 \\
3.1 \leqslant 3 a+0.7 \leqslant 4.6 \\
\because 3 a+0.7 \text { is an integer } \\
3 a+0.7=4 \\
a=1.1
\end{array}
$$

In summary: $a=1.1$