Why are binary numbers ordered the way they are? Counting to 7 in binary looks like this:
0
1
10
11
100
101
110
111
The highest value is always to the left. But would it make more sense to to it like this? Is there a way that this was picked, or was it a random decision?
0
1
01
11
001
101
011
111
 A: It's an arbitrary convention that we write 42 to mean 4 tens and 2 ones, as opposed to 4 ones and 2 tens. Somewhere down the line it was decided, and we've been stuck with it ever since. The way binary numbers (base 2) are represented follows the convention for base 10 numbers: the binary number 110 represents 1 four, 1 two, and 0 ones.
The convention of writing the most significant bits first is called big-endian bit order, while the reverse convention is called little-endian.
A: You might as well have asked why are decimal numbers ordered the way they are, that is, "four hundred and forty two" is written like this:
442 (least significant digit to most significant digit from right to left).
It might seem counter-intuitive at first because Latin languages are written from left to right, however, if you investigate further you'll find that the modern number system was based on Arabic language (and then developed to be closer to what it is today), And Arabic is a language that's written from right to left. (correct me if I'm wrong though)
So this rule really follows any number system: significance of the digits is in ascending order from right to left. 
EDIT: Apparently (as per the comments) the right-to-left convention had even existed way earlier than that: http://www-groups.dcs.st-and.ac.uk/history/HistTopics/Babylonian_numerals.html
