7. The fractional part, integer part, and the number itself of a positive number form a geometric sequence, then this positive number is
7. $\frac{1}{2}(\sqrt{5}+1)$ Let the decimal part of this positive number be $x$, and the integer part be $n(0 \leqslant x < 1, n > 0)$; (2) $n^{2}=x(n+x)$. From $0 < x < 1$ and $n > 0$ we know $x=\frac{\sqrt{5}-1}{2}$, so the required positive number is $n+x=\frac{\sqrt{5}+1}{2}$.