— reading, writing & making sense of BIG numbers —
💡 What's this chapter about?
This chapter helps us read, write & compare very large numbers
(lakhs, crores, millions, billions) using the Indian &
American (International) place value systems — and get a real
"feel" for how big they actually are!
🌾 1. What is One Lakh?
1,00,000 is called One Lakh → smallest 6-digit number
Written as 1 followed by 5 zeroes
Comma placed between "ten thousands" & "one lakh" place (Indian System)
999 largest 3-digit
+1 →
1,000 smallest 4-digit
…→
99,999 largest 5-digit
+1 →
1,00,000 = ONE LAKH!
📝 Pattern: largest (n)-digit number + 1 = smallest (n+1)-digit number
⚖️ Is a Lakh Big or Small?
Feels BIG 🌟
1 lakh rice varieties = huge diversity
1 lakh days ≈ living 274 years!
1 lakh people in a line ≈ 38 km long
Feels small 🔎
Cricket stadium seats 1 lakh+ people easily
We have 80,000–1,20,000 hairs on our head
Some fish lay ~1 lakh eggs at once!
👉 It depends on WHAT we compare it to — context matters!
🌍 2. Indian System vs American System
Indian system groups digits as 3-2-2-2… (thousand, lakh, crore) |
American groups as 3-3-3-3… (thousand, million, billion)
Indian System
Number
American System
One Thousand
1,000
One Thousand
Ten Thousand
10,000
Ten Thousand
One Lakh
1,00,000
Hundred Thousand
Ten Lakh
10,00,000
One Million
One Crore
1,00,00,000
Ten Million
Ten Crore
10,00,00,000
Hundred Million
One Arab
1,00,00,00,000
One Billion
1 lakh = 1 followed by 5 zeroes
1 crore = 1 followed by 7 zeroes
A lakh = 100 × thousand | A crore = 100 × lakh | An arab = 100 × crore
Words "lakh" & "crore" come from Sanskrit: lakṣha & koṭi
🎯 3. Exact vs Approximate Values
Sometimes exact numbers aren't needed — a rounded-off value gives enough idea of size!
🔺 Round UP when we need "enough" of something
e.g. 732 people → order 750 sweets (not 700!)
🔻 Round DOWN when giving a cautious/modest estimate
e.g. ₹470 item → "around ₹450"
✦ Nearest Neighbours ✦
Example: 6,72,85,183
Nearest
Value
Thousand
6,72,85,000
Ten Thousand
6,72,90,000
Lakh
6,73,00,000
Ten Lakh
6,70,00,000
Crore
7,00,00,000
⚡ 4. Multiplication Shortcuts (Patterns in Products)
Multiply by 5 → ×10 then ÷2 e.g. 116×5 = 116×10÷2 = 580
Multiply by 25 → ×100 then ÷4 e.g. 824×25 = 824×100÷4 = 20,600
Rearranging factors (commutative trick) makes big multiplications quick!
e.g. 2×1768×50 = (2×50)×1768 = 100×1768
✦ Digits in a Product ✦
Multiplying
Product has
2-digit × 1-digit
2-digit or 3-digit
2-digit × 2-digit
3-digit or 4-digit
3-digit × 3-digit
5-digit or 6-digit
Rule of 👍: min digits = sum of digits − 1, max digits = sum of digits
📏 5. Getting a "Feel" of Large Numbers
Compare unfamiliar big quantities to something familiar — like Somu (1 m tall)!
🗽 Statue of Unity ≈ 180 m
💦 Kunchikal Waterfall ≈ 450 m
🌍 Earth–Sun distance ≈ 15 crore km
🌙 Earth–Moon distance ≈ 3,84,400 km
💭 Trick: break big calculations into smaller stages — easier & less error-prone!
🧮 Quick Reference — Place Values
1 Lakh 10⁵
→
1 Crore 10⁷
→
1 Arab 10⁹
1 Million 10⁶
→
1 Billion 10⁹
10,000 lakh = 1 billion!
✦ ✦ ✦ QUICK REVISION CHECKLIST ✦ ✦ ✦
I can write 1 lakh & 1 crore with correct zeroes
I know the Indian comma pattern (3-2-2-2)
I know the American comma pattern (3-3-3-3)
I can convert Indian ↔ American systems
I can round numbers to nearest thousand/lakh/crore