Consider the numbers in binary. Each child will be the parent number with a 0 or 1 appended to it depending on whether it is left or right.
This means that everything to the left of the root will start 10 in binary and anything to the right will start 11 in binary.
This means that you should be able to work out which side it is on just using some shift operations and then some comparisons.
I should note that I don't know if this is the most efficient method but it is a easy to determine mathematical property of the left subtree.
As noted by others the consequence of the 0 or 1 appendation means that each digit encodes the path through the subtree. The first 1 represents the root of the tree and from then on a 0 will mean taking the left branch at that point and a 1 will mean taking the right branch.
Thus binary 1001101 would mean left, left, right, right, left, right.
An obvious consequence of this is that the number of binary digits will determine exactly how deep in the tree that number is. so 1 is the top (1st) level. 10 would be at the second level (one choice made). my example 1001101 would be at the 7th level (six choices made). I should note that I'm unfamiliar with Binary tree terminology so not sure if the root would usually be considered the first or zeroth level which is why I am being explicit about number of choices made too.
One last observation in case it hasn't already been observed is that the numbers will also be assigned counting from top to bottom, left to right. So the first level is 1. The next is 2 on the left, 3 on the right. The level below that will go 4, 5, 6, 7 and then the row below that 8, 9, 10, 11, 12, 13, 14, 15 and so on. This isn't any more useful mathematically but if you are trying to visualise it may well help.