Zeros of Two Floor-Fraction Functions

Let $[x]$ and $\{x\}$ denote the integer and fractional parts of $x$.

1. Find the number of zeros of $f(x)=\sin^2[x]+\sin^2\{x\}-1$ on $[0,100]$. 2. Find the number of zeros of $g(x)=[x]\cdot\{x\}-\dfrac 13x-1$ on $[0,100]$.