एकं दश शतं चैव सहस्रमयुतं तथा लक्षं च नियुतं चैव कोटिरर्बुदमेव च।
वृन्दं खर्वो निखर्वश्च शङ्खः पद्मश्च सागरः अन्त्यं मध्यं परार्धं च दशवृद्ध्या यथाक्रमम्॥
Word-by-word Breakdown & Translation
Line 1:
एकम् = One (1)
दश = Ten (10)
शतम् = Hundred (100)
चैव = and also
सहस्रम् = Thousand (1,000)
अयुतम् = Ten Thousand (10,000)
तथा = and then / as well
Line 2:
लक्षम् = One Lakh / Hundred Thousand (1,00,000)
च = and
नियुतम् = Ten Lakhs / Million (10,00,000)
चैव = and also
कोटिः = Crore / Ten Million (1,00,00,000)
अर्बुदम् = One Hundred Million (Arbuda)
Line 3:
वृन्दम् = One Billion
खर्वः = Ten Billion
निखर्वः = Hundred Billion
च = and
शङ्खः = Trillion
पद्मः = Ten Trillion
सागरः = Hundred Trillion
Line 4:
अन्त्यम् = One Quadrillion
मध्यम् = Ten Quadrillion
परार्धम् = Hundred Quadrillion
च = and
दशशब्देन = With the word ‘ten’
यथाक्रमम् = In regular sequence/order
“One, ten, hundred, thousand, and ten thousand;
Lakh, million, crore, and arbuda;
Vrinda, kharva, nikharva, shanku, padma, and sagara;
Antya, madhyama, and parardha — all these increase by ten in succession.”
🧩 Analysis:
Sequential Order:
The shloka gives a systematic list of Sanskrit number names in increasing order by a factor of 10 each.
Mnemonic Device:
The shloka is composed in a metrical form, making it easy to memorize, especially for students or scholars in ancient times.
1. Origins of Place Value & Decimal System
Ancient Indian scholars were among the first in the world to use a base-10 (decimal) place value system, which is the foundation of the modern number system we use today.
They used names for powers of ten extending far beyond what most civilizations ever needed — up to 10^17 and even beyond.
This system is visible in Vedic texts, Puranas, and mathematical treatises like those by Aryabhata and Bhaskaracharya.
2. Mathematical Sophistication
While other ancient civilizations often stopped at thousands or tens of thousands, Sanskrit texts documented values like Ayutam (10,000), Laksham (100,000), Koti (10 million), up to Parārdham (10^17).
This vocabulary shows how comfortable Indian thinkers were with large-scale calculations, which was essential for astronomy, cosmology, architecture, and trade.
3. Cosmic and Philosophical Applications
Numbers like Padma and Parārdha are often found in Puranic cosmology — used to express immense timescales, like the age of the universe or duration of Yugas.
For instance, the concept of Kalpas and Yugas (epochs) includes billions of years, which required a robust naming system.
4. Poetic & Mnemonic Utility
The structured naming system was often taught using shlokas (verses) like the one in your image. This made it easier to memorize large values through rhythmic patterns — a classic method of oral tradition.
5. Legacy in Modern Math
This system, along with the invention of zero and place-value notation, was later passed on to Islamic scholars, and then to Europe, forming the basis of the modern numeral system.
The words like Lakh and Crore still survive today in Indian English and are directly inherited from this tradition.
🧠 In Summary
The Sanskrit numeral system reflects the deep intellectual tradition of ancient India, showing not only mathematical advancement but also a cosmic vision that required thinking in huge numbers. It’s both practical and philosophical, helping shape the numerical systems we use globally today.
