Question on Math.floor on negative number why do these return different results?
Math.floor(-1735)=-1735
Math.floor(-17.35*100)=-1736
 A: $-17.35$ is a floating point number which cannot be represented exactly.  Your experiment indicates that the actual representation is slightly less than $-17.35$, so on multiplying by $100$ you get a number slightly less than $-1735$, so the floor is $-1736$
A: If you output the value of $-17.35\cdot100$ you will see that it gives the seemingly wrong result:
$$-17.35\cdot100=-1735.0000000000002$$
(I tested this in Firefox, but other browsers should give the same result) 
This is due to a rounding error. $-17.35$ can not be expressed exactly in a binary floating point number, since its denominator (when the number is expressed as a reduced fraction) is not a power of two. 
A: This is a rounding issue.  It may seem counterintuitive that we should have rounding issues when the numbers are so "nice".  However, the numbers are not nice in binary, which is how they are stored.
If we were to represent 17.35 as an exact value in binary, we would end up with
$$
10001.010110011... = 10001.010\overline{1100}
$$
Where the bar denotes a repeating decimal.  The computer stores this in a sort of "scientific notation".  In particular, the number is stored as
$$
\overbrace{1.0001010110011\dots 0\color{red}{10}}^{\text{53 digits}} \times 10^{100}
$$
where the red digits at the end correspond to the tail $...001(100)$ being rounded up to $...010$.
The net result of this rounding up is that when the computer attempts to calculate $100 \times 17.35$, it uses the exact value $100$ and a value slightly higher than $17.35$, so that the resulting product is slightly higher that 1735.  So, $-100 \times 17.35$ comes out to slightly less than $-1735$, so that the floor function rounds it down to $-1736$.
A: This should explain the different behaviour for $-17.35$ and $-35.35$:
\begin{align}
-17.35 
&= (11000001100010101100110011001101)_{\tiny\mbox{IEEE 754}} \\
& = -17.350000381469727 \\
& < -17.35
\end{align}
and
\begin{align}
-35.35 
&= (11000010000011010110011001100110)_{\tiny\mbox{IEEE 754}} \\
&= -35.349998474121094 \\
&> -35.35
\end{align}
Note: These are 32-bit representations, for 64-bit I expect the same behaviour. 
