Power Play · Lesson 6 of 7
A Pinch of History
“Explore historical and modern naming systems for very large powers of 10.”
• Describe historical naming of very large powers of 10. • Compare Indian and International large-number systems. • Connect names such as lakh, crore, billion and trillion with powers of 10. • Recognise googol and googolplex as named enormous numbers. • Use powers of 10 as a common way to compare naming systems.
The chapter shows that naming enormous numbers has a long history. Indian mathematical and literary traditions developed extended names for powers of 10 far beyond everyday counting.
The textbook mentions the Lalitavistara, Mahaviracharya's Ganita-sara-sangraha, the Jaina work Amalasiddhi and a Pali grammar associated with Kāccāyana. Their naming systems show sustained interest in extremely large quantities.
Modern Indian and International number names follow different patterns, but powers of 10 make their sizes easy to compare.
Problem
How many times larger is one trillion than one billion?
- 1.One billion = 10⁹.
- 2.One trillion = 10¹².
- 3.10¹² ÷ 10⁹ = 10³ = 1000.
- 4.So a trillion is 1000 times a billion.
Problem
How many times larger is one kharab than one arab?
- 1.One arab = 10⁹.
- 2.One kharab = 10¹¹.
- 3.10¹¹ ÷ 10⁹ = 10² = 100.
- 4.So one kharab is 100 arab.
The chapter also introduces a googol, equal to 10¹⁰⁰, and a googolplex, equal to 10 raised to the power googol. These examples show why exponent notation is essential when a number contains far too many zeros to write conveniently.
Quiz
One crore equals:
One billion equals:
10¹² is how many times 10⁹?
A googol is:
Why are powers of 10 useful across naming systems?
Practice Problems
- Write lakh, crore, arab, kharab and padma as powers of 10.
- Write million, billion, trillion and quadrillion as powers of 10.
- How many times larger is padma (10¹⁵) than crore (10⁷)?
- Compare one kharab (10¹¹) with one billion (10⁹).
- Explain why exponent notation is more practical than writing every zero in a googol.
Key Takeaways
• Historical Indian texts developed names for extremely large powers of 10. • Indian and International naming systems use different word patterns. • Powers of 10 provide a common language for comparison. • lakh=10⁵, crore=10⁷, arab=10⁹ and kharab=10¹¹. • million=10⁶, billion=10⁹ and trillion=10¹². • A googol is 10¹⁰⁰.