Under this system, the digits for 1 to 9 appeared as
and the first nine multiples of 10 appeared as
These symbols are alternated for successive powers of 10:
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There were two schemes of notation in use in ancient China.
Under this system, the digits for 1 to 9 appeared as
and the first nine multiples of 10 appeared as
These symbols are alternated for successive powers of 10:
Using this notation numbers as large as desired could be represented.
For example, 635,814 would appear as
The problem with this notation is the potential for ambiguity representing numbers with zeros in them. For example,
could read as 18, or 1008, or 100008. To rectify this, a place in which a zero was required was left blank, however this did not fully solve the problem as it was not necessarily obvious how many zeros a certain gap represented. In around the 13th Century, a round symbol O appeared for zero, and so 4096 was written as
Under this scheme, the multiplicative principle is used. There were distinct symbols for the digits from 1 to 9, and additional symbols for the powers of ten:
The digits from 1 to 9 would be multiplied by the power of ten which follows it, and so 647 would be written as
100 + 4 10 + 7Note that this eliminates the ambiguity described above, as if a certain power of 10 has no value, then it is simply ommitted. For example, 2030 would be written as
