In rounding with significant figures, you want to avoid undue precision, yes, but it's also important to minimize error. It's this error minimization which is the primary goal of all "round to nearest" approaches.
So in short:
\begin{align}
0.383 - 0.3825525 &= 0.0004475\\
0.3825525 - 0.382 &= 0.0005525
\end{align}
$0.0004475$ is less than $0.0005525$, so you should round up to $0.383$, as that's the nearest value, and will minimize any error you introduce by rounding.
Even & Odd?
So what's this about the even/odd rule? Is there any validity there?
This technique is called "Banker's rounding" and is also attempting to minimize error.
When a number falls exactly in the middle of the two values to be rounded to (that is, when the digit to round is "5" exactly), each of the two difference is equally far away. So to a first order, both will result in an equal amount of error.
But picking a consistent direction (e.g. "always round up") introduces a subtle bias in the sums over the long run. This is because the errors are biased.
. | Always | Up | Banker's | Banker's |
Value | Round Up | Error | Rounding | Error |
------+----------+-------+---------+------+
2.0 | 2 | 0.0 | 2 | 0.0 |
2.1 | 2 | -0.1 | 2 | -0.1 |
2.2 | 2 | -0.2 | 2 | -0.2 |
2.3 | 2 | -0.3 | 2 | -0.3 |
2.4 | 2 | -0.4 | 2 | -0.4 |
2.5 | 3 | +0.5 | 2 | -0.5 | <<<<<
2.6 | 3 | +0.4 | 3 | +0.4 |
2.7 | 3 | +0.3 | 3 | +0.3 |
2.8 | 3 | +0.2 | 3 | +0.2 |
2.9 | 3 | +0.1 | 3 | +0.1 |
3.0 | 3 | 0.0 | 3 | 0.0 |
3.1 | 3 | -0.1 | 3 | -0.1 |
3.2 | 3 | -0.2 | 3 | -0.2 |
3.3 | 3 | -0.3 | 3 | -0.3 |
3.4 | 3 | -0.4 | 3 | -0.4 |
3.5 | 4 | +0.5 | 4 | +0.5 | <<<<<
3.6 | 4 | +0.4 | 4 | +0.4 |
3.7 | 4 | +0.3 | 4 | +0.3 |
3.8 | 4 | +0.2 | 4 | +0.2 |
3.9 | 4 | +0.1 | 4 | +0.1 |
4.0 | 4 | 0.0 | 4 | 0.0 |
------+----------+-------+---------+-------+
63.0 | 64 | +1.0 | 63 | 0.0 | - Totals
With "always round up" you get a consistent $+0.5$ bias per decade, and this is consistent even if you extend the range to more decimal places. You can balance the errors for $0.00...01$ to $0.49...99$ with those for $0.99...99$ to $0.50...01$, but there's that dead center $0.50...00$ (aka $0.5$) which is the odd man out - consistent rounding up (or down) will introduce a bias because of this entry.
So what are you to do? Well, introduce a rule which rounds that entry up half the time and rounds down the other half. Bankers' rounding is the most common such rule. This rule says that if the digits to be rounded off are $5$ exactly, then round such that the last digit of the number after rounding is even. (Note that this is equivalent to a rule to round up if the digit to the left of the $5$ is odd, but round down if the digit to the left is even - two different ways of saying the same thing.)
0.255 -> 0.26 ... because 6 is even (or round up because 5 is odd)
0.265 -> 0.26 ... because 6 is even (or round down because 6 is even)
0.275 -> 0.28 ... because 8 is even (or round up because 7 is odd)
0.285 -> 0.28 ... because 8 is even (or round down because 8 is even)
But again, this is the rule only if the number to be rounded falls exactly between the two possibilities. If the number is closer to one or the other, then round to the nearest.
0.2453 -> 0.25 (Round to nearest)
0.2553 -> 0.26 (Round to nearest)
0.2651 -> 0.27 (Round to nearest)
0.275000 -> 0.28 (Falls exactly between 0.27 and 0.28, apply even/odd rules)
0.275378 -> 0.28 (Round to nearest)
0.285000 -> 0.28 (Falls exactly between 0.28 and 0.29, apply even/odd rules)
0.285023 -> 0.29 (Round to nearest)
Note also that you should only round once, and don't cascade your rounding:
0.14555 -> 0.1 (Round to nearest)
0.14555 -> 0.1456 -> 0.146 -> 0.15 -> 0.2 (WRONG!)
