📘 Large Numbers Around Us — Notes
🌍 1. Why Do We Need Large Numbers?
In daily life, we often deal with very big numbers, such as:
- Population of countries
- Distance between planets
- Money in national budgets
Writing these numbers fully can be confusing, so we use place value systems and short forms.
🔢 2. Place Value System (Indian System)
In the Indian system, digits are grouped differently from the international system.
📍 Place Value Chart (Indian System)
| Place | Value |
|---|---|
| Ones | 1 |
| Tens | 10 |
| Hundreds | 100 |
| Thousands | 1,000 |
| Ten Thousands | 10,000 |
| Lakhs | 1,00,000 |
| Ten Lakhs | 10,00,000 |
| Crores | 1,00,00,000 |
👉 Example:
5,23,45,678 = 5 crore 23 lakh 45 thousand 678
🌐 3. International Place Value System
Used in many countries like the USA.
| Place | Value |
|---|---|
| Ones | 1 |
| Thousands | 1,000 |
| Millions | 10,00,000 |
| Billions | 1,000,000,000 |
👉 Example:
5,23,45,678 (Indian) = 52,345,678 (International)
= 52 million 345 thousand 678
🔁 4. Converting Between Systems
Indian → International
- Remove Indian commas
- Place commas after every 3 digits from right
International → Indian
- First comma after 3 digits from right
- Then commas after every 2 digits
✍️ 5. Writing Large Numbers in Words
Steps:
- Separate periods (crores, lakhs, thousands, etc.)
- Write each part in words
- Combine them
👉 Example:
7,04,03,210
= Seven crore four lakh three thousand two hundred ten
📊 6. Estimation and Rounding Off
We often approximate numbers to make them easier to use.
Rules:
- If the next digit is 5 or more → round up
- If less than 5 → round down
👉 Example:
- 4,78,213 ≈ 4,80,000 (nearest lakh)
- 9,432 ≈ 9,000 (nearest thousand)
🧠 7. Comparing Large Numbers
To compare:
- Count number of digits
- More digits → larger number
- If equal digits, compare from left
👉 Example:
- 8,45,321 > 7,99,999
- 5,67,890 < 5,76,000
🌟 8. Use of Commas
Commas help in reading big numbers easily.
Indian System:
- 12,34,56,789
International System:
- 123,456,789
🌌 9. Large Numbers in Real Life
Examples:
- Population of India → over 140 crore
- Distance from Earth to Sun → about 150 million km
- National budgets → in lakhs and crores
📝 10. Key Points to Remember
- Indian system uses lakhs and crores
- International system uses millions and billions
- Always use commas correctly
- Practice reading and writing numbers in words
- Estimation helps in quick calculations
✅ Quick Practice
- Write in words: 3,45,67,890
- Convert to international system: 7,89,45,123
- Round off: 6,78,912 to nearest lakh
Large Numbers Around Us – Practice Questions
🔢 Section A: Basic Understanding (1–10)
- Write the number name of 4,56,789.
- Write in figures: Seven lakh twenty-three thousand five hundred.
- How many digits are there in 8,90,12,345?
- What is the place value of 7 in 3,47,921?
- Write the smallest 6-digit number.
- Write the largest 5-digit number.
- Expand 6,45,210.
- Write 900000 in words.
- Identify the digit in the thousands place in 5,67,890.
- Write the successor of 9,99,999.
🌍 Section B: Indian & International System (11–20)
- Write 45,67,890 in the international system.
- Write 23,456,789 in the Indian system.
- Express 7,000,000 in Indian system.
- Write 5 crore in numbers.
- Convert 8 million into Indian system.
- Write 9,87,65,432 in international form.
- How many lakhs are there in 10 million?
- Write 1 billion in Indian system.
- Write 6,50,00,000 in words (Indian system).
- Write 32,456,789 in words (international system).
🔁 Section C: Place Value & Expansion (21–30)
- Find the place value of 5 in 7,54,321.
- Write expanded form of 9,08,76,543.
- What is the value of 3 in 3,00,45,678?
- Write 2,34,56,789 in expanded notation.
- Which digit is in the lakh place in 8,76,54,321?
- Find the difference between place value and face value of 9 in 9,87,654.
- Write the number formed by digits: 5 in lakh place, 3 in thousand place, 7 in ones place.
- Write the number when 4 is in crore place and 2 is in thousand place.
- Write expanded form of 1,02,03,004.
- Identify the digit with highest place value in 7,65,43,210.
📊 Section D: Comparison & Ordering (31–40)
- Compare: 5,67,890 ___ 5,76,809
- Which is greater: 8,90,123 or 8,09,321?
- Arrange in ascending order:
4,56,789; 4,65,789; 4,56,879 - Arrange in descending order:
9,87,654; 9,78,654; 9,87,645 - Which is smallest: 7,65,432; 7,56,432; 7,65,423?
- Compare: 10,00,000 ___ 9,99,999
- Arrange: 2,34,567; 23,45,678; 2,03,456
- Which is greater: 6 million or 60 lakh?
- Compare: 1 crore ___ 10 million
- Arrange the numbers: 5 crore, 50 lakh, 5000
🔄 Section E: Rounding & Estimation (41–50)
- Round 4,56,789 to nearest thousand.
- Round 8,76,543 to nearest lakh.
- Round 9,99,999 to nearest lakh.
- Estimate 5,43,210 to nearest ten thousand.
- Round 7,89,456 to nearest thousand.
- Round 3,21,678 to nearest lakh.
- Estimate 1,49,999 to nearest lakh.
- Round 6,50,499 to nearest thousand.
- Estimate 2,75,349 to nearest ten thousand.
- Round 9,01,234 to nearest lakh.
Answers with Solutions
🔢 Section A: Basic Understanding (1–10)
1. 4,56,789
👉 Four lakh fifty-six thousand seven hundred eighty-nine
2. Seven lakh twenty-three thousand five hundred
👉 7,23,500
3. 8,90,12,345
👉 Total digits = 8
4. Place value of 7 in 3,47,921
👉 7 is in thousand place → 7,000
5. Smallest 6-digit number
👉 1,00,000
6. Largest 5-digit number
👉 99,999
7. 6,45,210 (Expanded form)
👉 6,00,000 + 40,000 + 5,000 + 200 + 10
8. 900000 in words
👉 Nine lakh
9. Thousands place in 5,67,890
👉 Digit = 7
10. Successor of 9,99,999
👉 10,00,000
🌍 Section B: Indian & International System (11–20)
11. 45,67,890
👉 4,567,890
12. 23,456,789
👉 2,34,56,789
13. 7,000,000
👉 70,00,000
14. 5 crore
👉 5,00,00,000
15. 8 million
👉 80,00,000
16. 9,87,65,432
👉 98,765,432
17. 10 million
👉 100 lakh
18. 1 billion
👉 100 crore
19. 6,50,00,000
👉 Six crore fifty lakh
20. 32,456,789
👉 Thirty-two million four hundred fifty-six thousand seven hundred eighty-nine
🔁 Section C: Place Value & Expansion (21–30)
21. 5 in 7,54,321
👉 5 is in ten-thousand place → 50,000
22. 9,08,76,543
👉 9,00,00,000 + 8,00,000 + 70,000 + 6,000 + 500 + 40 + 3
23. Value of 3 in 3,00,45,678
👉 Crore place → 3,00,00,000
24. 2,34,56,789
👉 2,00,00,000 + 30,00,000 + 4,00,000 + 50,000 + 6,000 + 700 + 80 + 9
25. Lakh place in 8,76,54,321
👉 Digit = 6
26. Face value = 9
Place value = 9,00,000
👉 Difference = 8,99,991
27. Number formation
👉 5 lakh + 3 thousand + 7 = 5,03,007
28. 4 in crore place, 2 in thousand
👉 4,00,02,000
29. 1,02,03,004
👉 1,00,00,000 + 2,00,000 + 3,000 + 4
30. Highest place value in 7,65,43,210
👉 Digit 7 (crore place)
📊 Section D: Comparison & Ordering (31–40)
31. 5,67,890 < 5,76,809
32. 8,90,123 > 8,09,321
33. Ascending:
👉 4,56,789 < 4,56,879 < 4,65,789
34. Descending:
👉 9,87,654 > 9,87,645 > 9,78,654
35. Smallest:
👉 7,56,432
36. 10,00,000 > 9,99,999
37. Ascending:
👉 2,03,456 < 2,34,567 < 23,45,678
38. 6 million = 60 lakh
👉 Equal
39. 1 crore = 10 million
👉 Equal
40. Ascending:
👉 5000 < 50 lakh < 5 crore
🔄 Section E: Rounding & Estimation (41–50)
41. 4,56,789 ≈ 4,57,000 (nearest thousand)
42. 8,76,543 ≈ 9,00,000 (nearest lakh)
43. 9,99,999 ≈ 10,00,000
44. 5,43,210 ≈ 5,40,000
45. 7,89,456 ≈ 7,89,000
46. 3,21,678 ≈ 3,00,000
47. 1,49,999 ≈ 1,00,000
48. 6,50,499 ≈ 6,50,000
49. 2,75,349 ≈ 2,80,000
50. 9,01,234 ≈ 9,00,000