On an expansion numbers on Fibonacci's sequences

In this paper theorems on the expression of real numbers on Fibonacci sequence. It pay a special attention to “explicit formulas” and conditions of the uniqueness of such representations. We note that unifiing of an expression of a real number over inverse values of a multiplicaticative system permits to get the estimation of the form
$$ e-\sum_{k=0}^n\frac 1{k!}=\frac{x_n}{n!}, \frac 1{n+1}\leq x_n<\frac 1n. $$
Expressions of numbers over the sequence of inverse of Fibonacci numbers essentially uses these representation throw powers of “the gold section” $\varphi=\frac{1+\sqrt 5}{2}.$