Class 7 | Ganita Prakash | Chapter 1
📊 Large Numbers Around Us
Lakhs · Crores · Billions · Patterns in Products
🌾 1.1 — What is a Lakh?
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📖 The Story Begins...
Eshwarappa, a farmer from Karnataka, learns that India once had
1 Lakh varieties of rice 🌾 — but now only a handful remain.
His children Roxie and Estu wonder: "How big is 1 lakh really?"
How big is 1 Lakh?
1,00,000 = One Lakh
- Largest 3-digit number: 999 → add 1 → Smallest 4-digit: 1000
- Largest 4-digit number: 9999 → add 1 → Smallest 5-digit: 10,000
- Largest 5-digit number: 99,999 → add 1 → Smallest 6-digit: 1,00,000 ✨
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Is 1 Lakh Big or Small? 🤔
- 1 Lakh days of life = 274 years — very long!
- Cricket stadium in Ahmedabad seats > 1 lakh people — packed!
- Humans have 80,000 to 1,20,000 hairs — that's about 1 lakh hairs!
- 1 lakh people in a line = 38 km long!
Reading Large Numbers:
📌 In Indian system, we use commas like: 12,78,830
→ Read as: Twelve lakh seventy-eight thousand eight hundred thirty
📌 Comma pattern: 3 digits → 2 → 2 → 2... from right to left
(ones → thousands → lakhs → crores)
📌 In Indian system, we use commas like: 12,78,830
→ Read as: Twelve lakh seventy-eight thousand eight hundred thirty
📌 Comma pattern: 3 digits → 2 → 2 → 2... from right to left
(ones → thousands → lakhs → crores)
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🔢 1.2 — Land of Tens (Place Value)
🖩 The Calculator World!
In "Land of Tens", special calculators have only +1, +10, +100, +1000... buttons. This helps us understand place value!
In "Land of Tens", special calculators have only +1, +10, +100, +1000... buttons. This helps us understand place value!
| Calculator | Button | Presses to make 1 Lakh |
|---|---|---|
| 🔵 Tedious Tens | +10 | 10,000 times |
| 🟣 Handy Hundreds | +100 | 1,000 times |
| 🟡 Thoughtful Thousands | +1000 | 100 times |
| 🔴 Creative Chitti | +1, +10, +100... +10,00,000 | Many ways! |
Place Value Notation (Indian System):
Number: 5,72,836 = (5×1,00,000) + (7×10,000) + (2×1,000) + (8×100) + (3×10) + (6×1)
💡 Trick: The minimum number of button presses = the sum of all digits!
(e.g., 5072 → 5+0+7+2 = 14 clicks minimum!)
Number: 5,72,836 = (5×1,00,000) + (7×10,000) + (2×1,000) + (8×100) + (3×10) + (6×1)
Ten Lakhs
5
Lakhs
7
Ten-Thou
2
Thousands
8
Hundreds
3
Tens
6
💡 Trick: The minimum number of button presses = the sum of all digits!
(e.g., 5072 → 5+0+7+2 = 14 clicks minimum!)
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💰 1.3 — Of Crores and Crores!
From Lakh to Crore:
- 10 × lakh = 10,00,000 (Ten Lakhs)
- 100 × lakh = 1,00,00,000 = 1 Crore! 🎉
- 1 Crore = 1 followed by 7 zeros!
- 100 Crores = 1 Arab (hundred crores)
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🌍 Indian vs American Number System
| 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 Lakhs | 10,00,000 | One Million |
| One Crore | 1,00,00,000 | Ten Million |
| Ten Crore | 10,00,00,000 | Hundred Million |
| One Arab (100 Cr) | 1,00,00,00,000 | One Billion |
Comma Pattern:
🇮🇳 Indian: 3-2-2-2 ... from right → 1,23,45,678
🇺🇸 American: 3-3-3-3 ... from right → 123,456,78
📌 1 lakh = 1 followed by 5 zeros
📌 1 crore = 1 followed by 7 zeros
📌 1 billion = 1 followed by 9 zeros = 100 crore
🇮🇳 Indian: 3-2-2-2 ... from right → 1,23,45,678
🇺🇸 American: 3-3-3-3 ... from right → 123,456,78
📌 1 lakh = 1 followed by 5 zeros
📌 1 crore = 1 followed by 7 zeros
📌 1 billion = 1 followed by 9 zeros = 100 crore
Did You Know? 🌏
The Indian system (lakhs & crores) is used in: India, Bhutan, Nepal, Sri Lanka, Pakistan, Bangladesh, Maldives, Afghanistan, Myanmar
The words lakh and crore come from Sanskrit: lakṣha (लक्ष) and koṭi (कोटि)!
The Indian system (lakhs & crores) is used in: India, Bhutan, Nepal, Sri Lanka, Pakistan, Bangladesh, Maldives, Afghanistan, Myanmar
The words lakh and crore come from Sanskrit: lakṣha (लक्ष) and koṭi (कोटि)!
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≈ 1.4 — Exact & Approximate Values
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When do we use approximate values?
Very often, we don't need exact numbers — an approximation is enough!
Example: Population of Chintamani = 76,068
We say → "About 75,000" — easy to understand! ✅
Very often, we don't need exact numbers — an approximation is enough!
Example: Population of Chintamani = 76,068
We say → "About 75,000" — easy to understand! ✅
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| Type | When to use | Example |
|---|---|---|
| ⬆️ Round Up | When you need more than actual | 732 students → Order 750 sweets |
| ⬇️ Round Down | When you want to seem cheaper | ₹470 → advertise as ₹450 |
| 🎯 Exact | Money in banks, legal matters | Bank balance: ₹1,23,456.78 exactly |
Nearest Neighbours — Rounding Rules:
Example: Round 6,72,85,183 to the nearest...
📌 Rule: If the next digit ≥ 5 → round up; if < 5 → round down
Example: Round 6,72,85,183 to the nearest...
- Thousand: Look at hundreds → 6,72,85,000 or 6,72,85,000
- Lakh: Look at ten-thousands → 6,72,85,000
- Crore: Look at ten-lakh digit → 7,00,00,000
📌 Rule: If the next digit ≥ 5 → round up; if < 5 → round down
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✖️ 1.5 — Patterns in Products
🧮 Quick Multiplication Tricks:
Examples:
✅ 2 × 1768 × 50 = (2 × 50) × 1768 = 100 × 1768 = 1,76,800
✅ 125 × 40 × 8 × 25 = (125×8) × (40×25) = 1000 × 1000 = 10,00,000
✅ 72 × 125 = 72 × (1000÷8) = 9 × 1000 = 9,000
- Multiply by 5 = Multiply by 10 then ÷ 2
- Multiply by 25 = Multiply by 100 then ÷ 4
- Multiply by 125 = Multiply by 1000 then ÷ 8
Examples:
✅ 2 × 1768 × 50 = (2 × 50) × 1768 = 100 × 1768 = 1,76,800
✅ 125 × 40 × 8 × 25 = (125×8) × (40×25) = 1000 × 1000 = 10,00,000
✅ 72 × 125 = 72 × (1000÷8) = 9 × 1000 = 9,000
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🎵 Fascinating Fact!
Purandaradāsa, the legendary Carnatic music composer (15th century), is said to have composed 1250 × 380 = 4,75,000 kīrtanas!
That's Four Lakh Seventy-Five Thousand songs! 🎶
Purandaradāsa, the legendary Carnatic music composer (15th century), is said to have composed 1250 × 380 = 4,75,000 kīrtanas!
That's Four Lakh Seventy-Five Thousand songs! 🎶
How Many Digits in a Product?
📌 Rule: Product digits = A+B (max) or A+B-1 (min)
| A digits × B digits | Product has |
|---|---|
| 1-digit × 1-digit | 1 or 2 digits |
| 2-digit × 1-digit | 2 or 3 digits |
| 2-digit × 2-digit | 3 or 4 digits |
| 3-digit × 3-digit | 5 or 6 digits |
| m-digit × n-digit | (m+n-1) or (m+n) digits |
📌 Rule: Product digits = A+B (max) or A+B-1 (min)
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🤔 1.6 — Did You Ever Wonder?
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🌍 Earth to Sun Distance:
2100 × 70,000 = 14,70,00,000 km = about 147 million km!
(The farthest distance is about 152 million km)
2100 × 70,000 = 14,70,00,000 km = about 147 million km!
(The farthest distance is about 152 million km)
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🚂 Trans-Siberian Railway!
Moscow to Vladivostok — one of the world's longest train journeys!
Distance × speed × time = very large numbers in real life!
Moscow to Vladivostok — one of the world's longest train journeys!
Distance × speed × time = very large numbers in real life!
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🐋 Amazing Real World Numbers:
- Blue whale weight: ~1,50,000 kg (1.5 lakh kg!)
- Some fish can lay 1 lakh eggs at once!
- Your body has about 37 trillion cells!
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🦅 Bird Record Holders:
- Grey-headed Albatross: covers 900-1000 km/day, recorded 12,000 km trip
- Bar-tailed Godwit: flew non-stop 13,560 km from Alaska to Australia in ~11 days!
- That's about 1233 km/day → ~51 km per hour! ✈️
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📝 Quick Summary Cheatsheet
Lakh = ?
1,00,000
= 1 followed by
5 zeros 🔢
1,00,000
= 1 followed by
5 zeros 🔢
Crore = ?
1,00,00,000
= 1 followed by
7 zeros 💰
1,00,00,000
= 1 followed by
7 zeros 💰
Billion = ?
1,000,000,000
= 100 crores
= 10,000 lakhs 🌍
1,000,000,000
= 100 crores
= 10,000 lakhs 🌍
Round Off
≥5 → Round UP ⬆️
<5 → Round DOWN ⬇️
Makes life easy! 😄
≥5 → Round UP ⬆️
<5 → Round DOWN ⬇️
Makes life easy! 😄
| Number | Indian Name | American Name | Zeros |
|---|---|---|---|
| 1,000 | One Thousand | One Thousand | 3 |
| 1,00,000 | One Lakh | Hundred Thousand | 5 |
| 10,00,000 | Ten Lakhs | One Million | 6 |
| 1,00,00,000 | One Crore | Ten Million | 7 |
| 1,00,00,00,000 | One Arab / 100 Crore | One Billion | 9 |
⚡ Super Quick Tips:
- Indian comma pattern: 3-2-2-2 from right (12,34,56,789)
- American comma pattern: 3-3-3 from right (1,234,567,89)
- Product of m & n digit numbers has (m+n-1) to (m+n) digits
- Multiply by 5 = ×10 ÷ 2; by 25 = ×100 ÷ 4; by 125 = ×1000 ÷ 8
- Minimum button presses to get a number = sum of its digits!
🌟 Great job completing Chapter 1! 🌟
Made with ❤️ by @edugrown
Made with ❤️ by @edugrown