Chapter 1 — Large Numbers Around Us

Chapter 1 of Ganita Prakash (Class 7 Maths) is about large numbers — lakhs, crores, arabs, millions, and billions — exploring how to read, write, compare, round, and work with them through real-life contexts and multiplication patterns.

This chapter introduces students to large numbers in both the Indian naming system (lakh, crore, arab) and the American/International system (million, billion), using real-world contexts such as rice varieties, city populations, and astronomical distances. Students learn to place commas correctly in each system, round numbers up or down depending on context, find 'nearest neighbours' (nearest thousand, lakh, crore), and apply multiplication shortcuts by factorising numbers to use powers of 10. The chapter closes with thought experiments and puzzles that build intuition for how big — or small — large numbers really are.

1. 011 lakh (1,00,000) is 1 followed by 5 zeroes; in the Indian system commas are placed in a 3-2-2-2 pattern from right to left.
2. 021 crore (1,00,00,000) is 1 followed by 7 zeroes and equals 100 lakhs; 1 arab equals 100 crores (also written 1,000,000,000 = 1 billion in the American system).
3. 03The Indian naming system is also used in Bhutan, Nepal, Sri Lanka, Pakistan, Bangladesh, Maldives, Afghanistan, and Myanmar; the words 'lakh' and 'crore' come from the Sanskrit lakṣha and koṭi.
4. 04The American/International system groups digits in a 3-3-3-3 pattern: thousand, million, billion.
5. 05Rounding up means the approximated number is more than the actual number (e.g., ordering 750 sweets for 732 people); rounding down means it is less (e.g., quoting ₹450 for an item costing ₹470).
6. 06Finding 'nearest neighbours' means rounding a large number to the nearest thousand, ten thousand, lakh, ten lakh, or crore.
7. 07A multiplication shortcut: multiplying by 5 is the same as dividing by 2 and multiplying by 10; multiplying by 25 is the same as dividing by 4 and multiplying by 100.
8. 08The number of digits in the product of two numbers: the product of two 2-digit numbers can only be a 3- or 4-digit number (minimum 10×10=100, maximum just under 100×100=10,000).
9. 09The minimum number of button-presses on a place-value calculator to reach a number equals the sum of that number's digits — which is also how Indian place value notation works.
10. 10Real-world large numbers explored include: India's Statue of Unity at ~180 metres, Mumbai's population exceeding 1 crore 24 lakhs (2011 Census), and the Earth–Sun distance of approximately 2100 × 70,000 km.