Introduction

Numbers are a fundamental part of mathematics and daily life. From counting to complex calculations, understanding numbers lays the foundation for all future learning in math. This chapter introduces students to the world of large numbers and operations on them.

1. Comparing Numbers

To compare numbers:

• Count digits: More digits = greater number
• If same number of digits, compare from left to right

Using commas:

• Indian System: 1,00,000; 10,00,000
• International System: 100,000; 1,000,000

2. Large Numbers in Practice

We see large numbers in population data, astronomy, finance, etc.

Examples:

• Indian: 12,34,56,789 → 12 crores 34 lakhs 56 thousand 789
• International: 123,456,789 → One hundred twenty-three million...

3. Estimation

Rounding Off

• Nearest 10: 64 → 60, 68 → 70
• Nearest 100: 349 → 300, 368 → 400
• Nearest 1000: 1628 → 2000, 1432 → 1000

Estimating Sums and Differences

578 + 243 ≈ 600 + 200 = 800

4. Using Brackets

Brackets indicate which operations to do first.

Example:

5 × (3 + 2) = 25
5 × 3 + 2 = 17

5. Roman Numerals

Symbol	Value
I	1
V	5
X	10
L	50
C	100
D	500
M	1000

Examples: IX = 9, XL = 40, CXL = 140

6. Place Value

Indian System: Ones, Tens, Hundreds, Thousands, Lakhs, Crores

Expanded Form: 5283 = 5000 + 200 + 80 + 3

7. Face Value and Place Value

Face Value: digit itself

Place Value: digit × position value

Example: In 5834, 8 has place value 800

8. Forming Numbers

• Greatest: Descending order of digits
• Smallest: Ascending order (0 cannot be first)

Example: 3, 0, 5, 2 → Greatest = 5320, Smallest = 2035

9. Properties of Numbers

• Commutative: a + b = b + a
• Associative: (a + b) + c = a + (b + c)
• Distributive: a × (b + c) = a × b + a × c

10. Operations with Large Numbers

Use standard methods for addition, subtraction, multiplication, and division.

11. Estimating Products and Quotients

Example: Estimate 894 × 37 ≈ 900 × 40 = 36,000

12. Introduction to Calculators

Calculators can help with large or difficult numbers but should be used wisely.

Real-Life Applications of Numbers

• Banking
• Shopping
• Travel
• Science
• Population Data

Practice Problems

1. Greatest and smallest 4-digit number from 3,0,5,9
2. Expanded form of 52,073
3. Round 478 to nearest 100
4. Add: 34876 + 20958
5. Multiply: 634 × 9
6. Roman Numerals: 49, 75, 99
7. Solve using brackets: 5 + 3 × (10 − 6)
8. Write 10 lakh in international system

Key Points to Remember

• Understand place value and face value
• Different numeration systems (Indian vs International)
• Estimation is helpful
• Roman numeral rules
• Properties: Commutative, Associative, Distributive

Conclusion

This chapter builds the foundation for understanding numbers, their use, and their representation. With regular practice, students gain confidence in handling large numbers and performing arithmetic operations.