Rules for rounding (positive and negative numbers) I'm looking for clear mathematical rules on rounding a number to $n$ decimal places.
Everything seems perfectly clear for positive numbers. Here is for example what I found on math.about.com :

Rule One Determine what your rounding digit is and look to the right side of it. If that digit is $4, 3, 2, 1,$ or $0$, simply drop all digits to the right of it.
Rule Two Determine what your rounding digit is and look to the right side of it. If that digit is $5, 6, 7, 8,$ or $9$ add $1$ to the rounding digit and drop all digits to the right of it.

But what about negative numbers ? Do I apply the same rules as above ?
For instance, what is the correct result when rounding $-1.24$ to $1$ decimal place ? $-1.3$ or $-1.2$ ?

"Round to nearest integer" is completely unambiguous, except when the fractional part of the number to be rounded happens to be exactly $\frac 1 2$.  In that case, some kind of tie-breaking rule must be used. Wikipedia (currently) lists six deterministic tie-breaking rules in more or less common use:


*

*Round $\frac 1 2$ up

*Round $\frac 1 2$ down

*Round $\frac 1 2$ away from zero

*Round $\frac 1 2$ towards zero

*Round $\frac 1 2$ to nearest even number

*Round $\frac 1 2$ to nearest odd number


Of these, I'm personally rather fond of "round $\frac 1 2$ to nearest even number", also known as "bankers' rounding".  It's also the default rounding rule for IEEE 754 floating-point arithmetic as used by most modern computers.  According to that rule,
$$\begin{aligned}
0.5 &\approx 0 & 1.5 &\approx 2 & 2.5 &\approx 2 & 3.5 &\approx 4 \\
-0.5 &\approx 0 & -1.5 &\approx -2 & -2.5 &\approx -2 & -3.5 &\approx -4. \\
\end{aligned}$$
