Key Learning Outcomes
By the end of this chapter, “Numbers and Numeration”, readers will:
- Indian Place Value System
- International Place Value System
- Comparing and Ordering Numbers
- Expanding Numbers (Expanded Form)
- Forming Greatest and Smallest Numbers
- Rounding Off Numbers
- Roman Numerals
- Use of Commas in Numbers
- Practice Questions with Solutions
Click On The Name To Go To A Specific Topic:
Introduction
The chapter “Numbers and Numeration” builds the foundation of mathematics. It teaches students how to read, write, compare, and understand large numbers in both the Indian and International number systems. It also covers place value, face value, and expanded form, which are essential for advanced calculations.
A number is a mathematical symbol used to count, measure, and label.
In Class 5, students learn about numbers up to 9-digit or 10-digit levels.
👉 Example:
- 1-digit number: 5
- 2-digit number: 23
- 6-digit number: 789023
Indian Place Value System
The Indian Place Value System uses periods like ones, thousands, lakhs, and crores.
| Period | Place Values |
|---|---|
| Ones | Ones, Tens, Hundreds |
| Thousands | Thousands, Ten Thousands |
| Lakhs | Lakhs, Ten Lakhs |
| Crores | Crores, Ten Crores |
Example:
Number: 2,47,85,930
Reading: Two crore forty-seven lakh eighty-five thousand nine hundred thirty.
Hinglish Tip:
“Comma use helps: 2,47,85,930 ko 2 crore, 47 lakh, 85 hazar, 930 kehte hain.”
International Place Value System
This system uses ones, thousands, millions, billions, etc.
| Period | Place Values |
|---|---|
| Ones | Ones, Tens, Hundreds |
| Thousands | Thousands, Ten Thousands, Hundred Thousands |
| Millions | Millions, Ten Millions, Hundred Millions |
Example:
Number: 24,785,930
Reading: Twenty-four million seven hundred eighty-five thousand nine hundred thirty.
Comparing and Ordering Numbers
- To compare numbers, start from the leftmost digit.
- The number with more digits is greater.
Example:
Compare: 78,654 and 87,654 → 87,654 is greater.
Expanded Form
Writing a number by showing the value of each digit.
Example:
Number: 5,23,417
Expanded Form: 5,00,000 + 20,000 + 3,000 + 400 + 10 + 7
Forming Greatest and Smallest Numbers
Using given digits once only, arrange:
- Greatest Number: in descending order
- Smallest Number: in ascending order (avoid zero at the beginning)
Example:
Digits: 3, 0, 7, 8
- Greatest: 8730
- Smallest: 3078
Rounding Off Numbers
Used for approximation.
Rules:
- If the digit is 5 or more, round up
- If the digit is less than 5, round down
Example:
Round 6,847 to nearest hundred = 6,800
Round 6,847 to nearest thousand = 7,000
Roman Numerals
Roman Numerals are based on combinations of letters from the Latin alphabet.
| Symbol | Value |
|---|---|
| I | 1 |
| V | 5 |
| X | 10 |
| L | 50 |
| C | 100 |
| D | 500 |
| M | 1000 |
Example:
- IV = 4
- XL = 40
- XC = 90
- CXX = 120
Use of Commas in Numbers
In the Indian System, commas are placed:
- After 3 digits from the right → then every 2 digits
Example: 56,78,943
In the International System, commas are placed:
- After every 3 digits from the right
Example: 5,678,943
Important Facts:
- 1 lakh = 100,000
- 1 crore = 10,000,000
- Roman numerals don’t use zero
- Numbers can be grouped in periods for easier reading
Activity (Exercise):
A. Fill in the blanks:
- 1 lakh = _____ thousands.
- The Roman numeral for 49 is _____.
- In the number 6,45,320 digit at ten thousand place = _______.
B. Write in Expanded Form:
- 3,42,601
- 45,67,890
C. Write in Numerals:
- Seventy-eight lakh twenty-one thousand nine hundred twelve
D. Compare the numbers using >, < or =
- 6,43,210 _ 6,34,210
Quiz:
Coming Soon…
Supplementary Materials:
Provide downloadable materials for learners to review:
- – PDF Guide: “Coming Soon”
- – Cheat Sheet: “Coming Soon”
- – Video Source: “JNG ACADEMY“
- – Articles: “Blog Page“