Indian Number System

Introduction

Numbers are essential in our life. Counting with numbers is required in our day to day transactions. What is the population of our country? How many members are affected with the pandemic? What is the temperature in the city ? What is the distance between two cities ? What is the cost of the daily essentials ? These are the questions coming as part of our life. Answers to these questions will be in numbers only.

Let us see what these numbers are and how did they originate?

Counting starts from the number One. Zero is a number which precedes number One. The Numbers from 0 to 9 which we use for counting have an interesting history.

The Indian Numerals

India has a very ancient history dating back to thousands of years. In those days Samskrit was commonly used.

Numbers	Sanskrit Name	Numbers	Sanskrit Name
1	ekam	10+1 = 11	ekādaśa
2	dve	10+5 = 15	pañcadaśa
3	trīṇi	10+10 =20	viṃśatiḥ
4	catvāri	50	pañcāśat
5	pañca	100	śatam
6	ṣaṭ
7	sapta
8	aṣṭa
9	nava
10	daśa

While the Greeks had no terminology for denominations above the myriad (10⁴) and the Romans above the mille (10³) , the ancient Hindus dealt freely with no less than eighteen denominations. In modern times also, the numeral language of no other nation is as scientific and perfect as that of the Hindus.

In the Yaurveda Saṃhitā (Vājasaneyi) the following list of numeral 'denominations is given: Eka (1), daśa (10), śata (100), sahasra (1000), ayuta (10,000), niyuta (100,000), prayuta (1,000,000), arbuda (10,000,000), nyarbuda (100,000,000), samudra (1,000,000,000), madhya (10,000,000,000), anta (100,000,000,000), parārdha (1,000,000,000,000). The same list occurs at two places in the Taittirīya Saṃhitā .

Decimal Place Value System

Āryabhaṭa uses the phrase ' स्थानात् स्थानं दशगुणं स्यात् ' to explain the place value system. This means "the number from place to place is ten times the preceding one." To understand the place value system, the digits when placed from right to left occupy a certain position. Starting from right, the first digit will occupy the first position, the second digit will occupy the second position, the third digit will occupy the third position and so on. From the second position onwards the value of each place increases by ten. Hence every digit placed one place away from right side has its value increased by ten times. Since the value of the digits increases by ten, it is called the 'decimal' place value system.

For example consider the number 567 which is equal to 500 + 60 +7 = 5 X 100 + 6 X 10 + 7 X 1

5	6	7
↑	↑	↑
Hundreds	Tens	Units

Āryabhaṭa I (499) says on the names of the position as "Eka (unit), daśa (ten), śata (hundred), sahasra (thousand), ayuta (ten thousand), niyuta (hundred thousand), prayuta (million), koṭi (ten million), arbuda (hundred million) and vṛnda (thousand million) are respectively from place to place each ten times the preceding".

Śrīdhara (750) has given the following names : Eka (Unit), daśa (ten), śata (hundred), sahasra (thousand), ayuta (ten thousand), lakṣa (lakh), prayuta (ten lakhs), koṭi (crore), arbuda (ten crore), abja (hundred crore), kharva (thousand crore), nikharva (ten thousand crore), mahāsaroja (one lakh crore) , Śaṅkhu (ten lakh crore)

See Also

भारतीय संख्या प्रणाली