Class 7 | Ganita Prakash | Chapter 1
๐ Large Numbers Around Us
Lakhs ยท Crores ยท Billions ยท Patterns in Products
๐พ 1.1 โ What is a Lakh?
@edugrown
@edugrown
๐ The Story Begins...
Eshwarappa, a farmer from Karnataka, learns that India once had
1 Lakh varieties of rice ๐พ โ 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 โ add 1 โ Smallest 4-digit: 1000
- Largest 4-digit number: 9999 โ add 1 โ Smallest 5-digit: 10,000
- Largest 5-digit number: 99,999 โ add 1 โ Smallest 6-digit: 1,00,000 โจ
@edugrown
Is 1 Lakh Big or Small? ๐ค
- 1 Lakh days of life = 274 years โ very long!
- Cricket stadium in Ahmedabad seats > 1 lakh people โ packed!
- Humans have 80,000 to 1,20,000 hairs โ that's about 1 lakh hairs!
- 1 lakh people in a line = 38 km long!
Reading Large Numbers:
๐ In Indian system, we use commas like: 12,78,830
โ Read as: Twelve lakh seventy-eight thousand eight hundred thirty
๐ Comma pattern: 3 digits โ 2 โ 2 โ 2... from right to left
(ones โ thousands โ lakhs โ crores)
๐ In Indian system, we use commas like: 12,78,830
โ Read as: Twelve lakh seventy-eight thousand eight hundred thirty
๐ Comma pattern: 3 digits โ 2 โ 2 โ 2... from right to left
(ones โ thousands โ lakhs โ crores)
ใฐ๏ธใฐ๏ธใฐ๏ธ
๐ข 1.2 โ Land of Tens (Place Value)
๐ฉ 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 |
|---|---|---|
| ๐ต Tedious Tens | +10 | 10,000 times |
| ๐ฃ Handy Hundreds | +100 | 1,000 times |
| ๐ก Thoughtful Thousands | +1000 | 100 times |
| ๐ด Creative Chitti | +1, +10, +100... +10,00,000 | Many ways! |
Place Value Notation (Indian System):
Number: 5,72,836 = (5ร1,00,000) + (7ร10,000) + (2ร1,000) + (8ร100) + (3ร10) + (6ร1)
๐ก Trick: The minimum number of button presses = the sum of all digits!
(e.g., 5072 โ 5+0+7+2 = 14 clicks minimum!)
Number: 5,72,836 = (5ร1,00,000) + (7ร10,000) + (2ร1,000) + (8ร100) + (3ร10) + (6ร1)
Ten Lakhs
5
Lakhs
7
Ten-Thou
2
Thousands
8
Hundreds
3
Tens
6
๐ก Trick: The minimum number of button presses = the sum of all digits!
(e.g., 5072 โ 5+0+7+2 = 14 clicks minimum!)
ใฐ๏ธใฐ๏ธใฐ๏ธ
๐ฐ 1.3 โ Of Crores and Crores!
From Lakh to Crore:
- 10 ร lakh = 10,00,000 (Ten Lakhs)
- 100 ร lakh = 1,00,00,000 = 1 Crore! ๐
- 1 Crore = 1 followed by 7 zeros!
- 100 Crores = 1 Arab (hundred crores)
@edugrown
@edugrown
ใฐ๏ธใฐ๏ธใฐ๏ธ
๐ 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:
๐ฎ๐ณ Indian: 3-2-2-2 ... from right โ 1,23,45,678
๐บ๐ธ American: 3-3-3-3 ... from right โ 123,456,78
๐ 1 lakh = 1 followed by 5 zeros
๐ 1 crore = 1 followed by 7 zeros
๐ 1 billion = 1 followed by 9 zeros = 100 crore
๐ฎ๐ณ Indian: 3-2-2-2 ... from right โ 1,23,45,678
๐บ๐ธ American: 3-3-3-3 ... from right โ 123,456,78
๐ 1 lakh = 1 followed by 5 zeros
๐ 1 crore = 1 followed by 7 zeros
๐ 1 billion = 1 followed by 9 zeros = 100 crore
Did You Know? ๐
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: lakแนฃha (เคฒเคเฅเคท) and koแนญi (เคเฅเคเคฟ)!
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: lakแนฃha (เคฒเคเฅเคท) and koแนญi (เคเฅเคเคฟ)!
ใฐ๏ธใฐ๏ธใฐ๏ธ
โ 1.4 โ Exact & Approximate Values
@edugrown
When do we use approximate values?
Very often, we don't need exact numbers โ an approximation is enough!
Example: Population of Chintamani = 76,068
We say โ "About 75,000" โ easy to understand! โ
Very often, we don't need exact numbers โ an approximation is enough!
Example: Population of Chintamani = 76,068
We say โ "About 75,000" โ easy to understand! โ
@edugrown
@edugrown
| Type | When to use | Example |
|---|---|---|
| โฌ๏ธ Round Up | When you need more than actual | 732 students โ Order 750 sweets |
| โฌ๏ธ Round Down | When you want to seem cheaper | โน470 โ advertise as โน450 |
| ๐ฏ Exact | Money in banks, legal matters | Bank balance: โน1,23,456.78 exactly |
Nearest Neighbours โ Rounding Rules:
Example: Round 6,72,85,183 to the nearest...
๐ Rule: If the next digit โฅ 5 โ round up; if < 5 โ round down
Example: Round 6,72,85,183 to the nearest...
- Thousand: Look at hundreds โ 6,72,85,000 or 6,72,85,000
- Lakh: Look at ten-thousands โ 6,72,85,000
- Crore: Look at ten-lakh digit โ 7,00,00,000
๐ Rule: If the next digit โฅ 5 โ round up; if < 5 โ round down
ใฐ๏ธใฐ๏ธใฐ๏ธ
โ๏ธ 1.5 โ Patterns in Products
๐งฎ Quick Multiplication Tricks:
Examples:
โ 2 ร 1768 ร 50 = (2 ร 50) ร 1768 = 100 ร 1768 = 1,76,800
โ 125 ร 40 ร 8 ร 25 = (125ร8) ร (40ร25) = 1000 ร 1000 = 10,00,000
โ 72 ร 125 = 72 ร (1000รท8) = 9 ร 1000 = 9,000
- Multiply by 5 = Multiply by 10 then รท 2
- Multiply by 25 = Multiply by 100 then รท 4
- Multiply by 125 = Multiply by 1000 then รท 8
Examples:
โ 2 ร 1768 ร 50 = (2 ร 50) ร 1768 = 100 ร 1768 = 1,76,800
โ 125 ร 40 ร 8 ร 25 = (125ร8) ร (40ร25) = 1000 ร 1000 = 10,00,000
โ 72 ร 125 = 72 ร (1000รท8) = 9 ร 1000 = 9,000
@edugrown
@edugrown
๐ต Fascinating Fact!
Purandaradฤsa, the legendary Carnatic music composer (15th century), is said to have composed 1250 ร 380 = 4,75,000 kฤซrtanas!
That's Four Lakh Seventy-Five Thousand songs! ๐ถ
Purandaradฤsa, the legendary Carnatic music composer (15th century), is said to have composed 1250 ร 380 = 4,75,000 kฤซrtanas!
That's Four Lakh Seventy-Five Thousand songs! ๐ถ
How Many Digits in a Product?
๐ Rule: Product digits = A+B (max) or A+B-1 (min)
| A digits ร B digits | Product has |
|---|---|
| 1-digit ร 1-digit | 1 or 2 digits |
| 2-digit ร 1-digit | 2 or 3 digits |
| 2-digit ร 2-digit | 3 or 4 digits |
| 3-digit ร 3-digit | 5 or 6 digits |
| m-digit ร n-digit | (m+n-1) or (m+n) digits |
๐ Rule: Product digits = A+B (max) or A+B-1 (min)
ใฐ๏ธใฐ๏ธใฐ๏ธ
๐ค 1.6 โ Did You Ever Wonder?
@edugrown
@edugrown
๐ Earth to Sun Distance:
2100 ร 70,000 = 14,70,00,000 km = about 147 million km!
(The farthest distance is about 152 million km)
2100 ร 70,000 = 14,70,00,000 km = about 147 million km!
(The farthest distance is about 152 million km)
@edugrown
@edugrown
๐ Trans-Siberian Railway!
Moscow to Vladivostok โ one of the world's longest train journeys!
Distance ร speed ร time = very large numbers in real life!
Moscow to Vladivostok โ one of the world's longest train journeys!
Distance ร speed ร time = very large numbers in real life!
@edugrown
@edugrown
๐ 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!
@edugrown
@edugrown
๐ฆ
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 โ ~51 km per hour! โ๏ธ
ใฐ๏ธใฐ๏ธใฐ๏ธ
๐ Quick Summary Cheatsheet
Lakh = ?
1,00,000
= 1 followed by
5 zeros ๐ข
1,00,000
= 1 followed by
5 zeros ๐ข
Crore = ?
1,00,00,000
= 1 followed by
7 zeros ๐ฐ
1,00,00,000
= 1 followed by
7 zeros ๐ฐ
Billion = ?
1,000,000,000
= 100 crores
= 10,000 lakhs ๐
1,000,000,000
= 100 crores
= 10,000 lakhs ๐
Round Off
โฅ5 โ Round UP โฌ๏ธ
<5 โ Round DOWN โฌ๏ธ
Makes life easy! ๐
โฅ5 โ Round UP โฌ๏ธ
<5 โ Round DOWN โฌ๏ธ
Makes life easy! ๐
| 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 |
โก 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 = ร10 รท 2; by 25 = ร100 รท 4; by 125 = ร1000 รท 8
- Minimum button presses to get a number = sum of its digits!
๐ Great job completing Chapter 1! ๐
Made with โค๏ธ by @edugrown
Made with โค๏ธ by @edugrown