For every real number $x$, let $\lfloor x\rfloor$ denote the greatest integer not exceeding $x$, and let $f(x)=\lfloor x\rfloor (10^{x-\lfloor x\rfloor }-1)$. The set of all numbers $x$ such that $1\le x<10$ and $f(x)\le 1$ is a union of disjoint intervals. What is the sum of the lengths of those intervals?