... The system of notation in the Bakhshali arithmetic [used in the Bakhshali manuscript written perhaps in the ninth century, but with contents composed 'no later than the fourth century AD'] is much the same as that employed in the arithmetical works of Brahmagupta and Bhaskara. There is, however, a very important exception. The sign for the negative quantity is a cross (+). It looks exactly like our modern sign for the positive quantity, but is placed after the number which it qualifies. Thus 

                      12                       7   +

                      1                         1

means 12 - 7 (i.e. 5). This is a sign which I have not met with in any other Indian arithmetic; nor, so far as I have been able to ascertain, is it now known in India at all. The sign now used is a dot placed over the number to which it refers. Here, therefore, there appears to be a mark of great antiquity.

The following statement, from the first example of the twenty-fifth sutra, affords a good example of the system of notation employed in the Bakhshali arithmetic:

                      l      1       1       1                                                                   

                      1       1       1       1    bha     32     phalam    108

                               3+     3+     3+ 

Here the initial dot is very much in the same way as we use the letter 'X' to denote the unknown quantity the value of which is sought. The number 1 under the dot is the sign of the whole (in this case, the unknown) number. A fraction is denoted by placing one number under the other without any line of separation; thus 

                      1

                      3

is 1/3, i.e. one-third. A mixed number is shown by placing the three numbers under one another; thus 

                      1

                      1

                      3

is 1 + 1/3 or 1 1/3, i.e. one and one-third. Hence 

                      1

                      1

                      3+ 

means 1 - 1/3 (i.e. 2/3). 

Multiplication is usually indicated by placing the numbers side by side; thus 

                      5                    32

                      8                    1      phalam     20 

means 5/8 * 32 = 20. Similarly 

                      1             1            1

                      1             1            1

                      3+           3+          3+ 

means 2/3 * 2/3 * 2/3 or (2/3)³, i.e. 8/27.  

Bha is an abbreviation of bhaga, 'part', and means that the number preceeding it is to be treated as a denominator. Hence 

                      1              1              1

                      1              1              1      bha

                      3+            3+            3+ 

means 1 : 8/27 or 27/8. The whole statement, therefore, means 27/8 * 32 = 108,  

                      l      1       1       1                                                                   

                      1       1       1       1    bha     32     phalam    108

                               3+     3+     3+ 

and may be thus explained - 'a certain number is found by dividing with 8/27 and multiplying with 32; that number is 108' ...

The dot is also used for another purpose, namely as one of the ten fundamental figures of the decimal system of notation, or the zero (0 1 2 3 4 5 6 7 8 9). It is still so used in India for both purposes, to indicate the unknown quantity as well as the nought. With us the dot, or rather its substitute the circle (0), has only retained the latter of its two intents, being simply the zero figure, or 'the mark of position' in the decimal system.  

The Indian usage, however, seems to show how the zero arose, and that it arose in India. The Indian dot, unlike our modern zero, is not properly a numerical figure at all. It is simply a sign to indicate an empty place or a hiatus. This is clearly shown by its name sunya 'empty' ...