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Systems of Numeration

Systems of Numeration

Let us begin with a discussion of some of the important systems of number- representation that prevailed in India.
Indians had separate names for the powers of ten, up to 17:-
eka = 1,

dasa = 10,

sata = 100- 10^2
, sahasra = 1000- 10^3

ayuta= 10,000 = 10^4,

niyuta (also called /aksa) = 100,000 = 10^5 prayuta =
1 ,QQQ,QQQ :106 , k0fi: 1 Q,QQQ,QQQ: 107 , arbuda = 1 QQ,QQQ,QQQ: 108 ,
abja (or vrinda) = 1,000,000,000 = 109
, kharva = 10,000,000,000 =
1010
, nikharva = 100,000,000,000 = 1011
, mahapadma =
1,000,000,000,000 = 1012
, sanku = 10,000,000,000,000 = 1 013
, jaladhi
=1 00,000,000,000,000 = 1014, antya = 1,000,000,000,000,000 = 1 015,=
madhya = 10,000,000,000,000,000 = 1016
, and parardha =
100,000,000,000,000,000 = 1017 [11; 16 & 61]
Even though several systems for expressing numbers sprouted
in ancient India, only a few gained any popularity and acceptability.
The Bhuta Samkhya system and the Katapayadi system were
two schemes which survived for a long time. Of these the Bhuta
Samkhya system seems to be the older one.
The Bhuta Samkhya System : Samkhya means number and
Bhuta element, part, component, number etc. In this system,
numbers are indicated by well-known objects or concepts having as
many parts or components as the numbers they connote eg.:
0 is denoted by sunya (void), kha (sky), antariksa (atmosphere),
puma (whole), randhra (hole) etc.
1 is denoted by sasi (moon). bhumi (earth), go (cow) etc.
2. is denoted by netra (eyes), bahu (hands), kama (ears),
paksa (moon’s waxing and waning periods) etc. – each of which has
a pair of members.