Chapter 1: Knowing Our Numbers (Based on NCERT Textbook)

🔶 What is This Chapter About?

This chapter helps us understand:

Big numbers
Place values
Comparison of numbers
Forming numbers
Use of commas
Estimation
Using numbers in daily life

🔢 1. Comparing Numbers

We compare numbers to find which is greater or smaller.

How to Compare:

Start from the leftmost digit.
The number with more digits is greater.
If digits are equal, compare digit by digit from left.

Example:
Which is greater: 5,367 or 6,245?
✅ 6,245 is greater.

🔤 2. Forming Numbers

We can form the largest or smallest number using given digits.

Steps:

For the largest number, arrange digits in descending order.
For the smallest number, arrange digits in ascending order (avoid zero at the start).

Example:
Digits: 3, 0, 9, 1

Greatest: 9,3,1,0 → 9310
Smallest: 1,0,3,9 → 1039

📍 3. Place Value (Indian and International System)

A. Indian Place Value System:

We group numbers as:

Ones, Tens, Hundreds
Thousands, Ten Thousands
Lakhs, Ten Lakhs, Crores

Example:
23,45,678 = 23 lakh 45 thousand 678

Place values:

Digit	Place	Value
2	Ten Lakh	20,00,000
3	Lakh	3,00,000
4	Ten Thousand	40,000
5	Thousand	5,000
6	Hundred	600
7	Ten	70
8	One	8

B. International Place Value System:

We group numbers as:

Ones, Tens, Hundreds
Thousands, Ten Thousands, Hundred Thousands
Millions, Ten Millions, Hundred Millions

Example:
5,462,190 = Five million four hundred sixty-two thousand one hundred ninety

🔘 4. Use of Commas

Commas help us read big numbers easily.

A. Indian System:

Commas are placed after:

3 digits from the right (for hundreds)
Then every 2 digits

Example: 12,34,567

B. International System:

Commas are placed after:

Every 3 digits from the right.

Example: 1,234,567

💰 5. Estimation

Estimation helps us to find approximate answers.

A. Rounding off numbers:

To the nearest 10
To the nearest 100
To the nearest 1000

Examples:

38 rounded to nearest 10 → 40
154 rounded to nearest 100 → 200
2670 rounded to nearest 1000 → 3000

B. Estimating in addition/subtraction:

Instead of exact answer, we use rounded numbers for quick calculation.

Example:
Estimate 677 + 243
→ Round off: 700 + 200 = 900

📏 6. Using Brackets

Brackets help group parts of an expression.

Examples:

Without bracket: 4 + 3 × 2 = 4 + 6 = 10
With bracket: (4 + 3) × 2 = 7 × 2 = 14

✅ Solve inside the bracket first.

💡 7. Roman Numerals

Romans used letters instead of numbers.

Symbols:

Roman	Hindu-Arabic
I	1
V	5
X	10
L	50
C	100
D	500
M	1000

Rules:

I before V or X → subtract (IV = 4, IX = 9)
I after V or X → add (VI = 6, XI = 11)

WORKSHEET

1. Fill in the blanks:

The place value of 7 in 87,654 is ________.
The largest number that can be formed with digits 3, 5, and 9 is ________.
67,450 rounded to the nearest 100 is ________.
In the number 9,87,654, the place value of 8 is ________.
The number 1,24,567 is read as ________.

2. True or False:

In the International System of Numeration, commas are placed after every 2 digits.
The number 4,56,789 can be written as 4.56 lakh in the Indian system.
999 rounded to the nearest 100 is 1000.
The place value of 5 in the number 75,325 is fifty thousand.
24,567 rounded to the nearest 1000 is 25,000.

3. Choose the correct option:

The greatest number you can make from digits 4, 1, 3, and 7 is:
- a) 7413
- b) 4731
- c) 7431
- d) 4173
The place value of 9 in 1,09,876 is:
- a) 9
- b) 90,000
- c) 9,000
- d) 900
54,987 rounded to the nearest 100 is:
- a) 55,000
- b) 54,900
- c) 54,800
- d) 50,000
In the number 3,45,678, the digit 5 stands for:
- a) Ten thousands
- b) Thousands
- c) Lakhs
- d) Hundreds

4. Match the following:

Column A	Column B
1. 1,25,789	a) 1000
2. 58,000	b) 1 Lakh Twenty-Five Thousand Seven Hundred Eighty-Nine
3. The place value of 2 in 4,52,100	c) 50 Thousand
4. 8,76,542	d) 200

5. Write the number:

Two lakh twenty-five thousand one hundred thirty-eight.
Five lakh seven thousand four hundred sixty-five.
One crore seventy-five thousand two hundred.

6. Estimate the sum:

456 + 789 (Estimate by rounding off to the nearest 100).
674 + 355 (Estimate by rounding off to the nearest 10).
2345 + 1587 (Estimate by rounding off to the nearest 1000).

7. Roman Numerals:

Write 78 in Roman Numerals.
Write 56 in Roman Numerals.
What is the Roman Numeral for 99?

8. Solve:

What is the place value of 6 in the number 56,739?
What is the smallest number that can be formed using the digits 4, 2, 1, and 7?
Round off 542 to the nearest 10, and write the result.

9. Number Formation:

Form the greatest and smallest 4-digit numbers from these digits: 3, 5, 1, 6.

Answers to the Worksheet:

Fill in the blanks:
1. 70,000
2. 953
3. 67,500
4. 80,000
5. One lakh twenty-four thousand five hundred sixty-seven
True or False:
1. False
2. True
3. False
4. True
5. False
Choose the correct option:
1. c) 7431
2. c) 9,000
3. b) 54,900
4. a) Ten thousands
Match the following:
1. b) 1 Lakh Twenty-Five Thousand Seven Hundred Eighty-Nine
2. c) 50 Thousand
3. a) 1000
4. d) 200
Write the number:
1. 2,25,138
2. 5,07,465
3. 1,75,200
Estimate the sum:
1. 456 + 789 → 500 + 800 = 1300
2. 674 + 355 → 670 + 360 = 1030
3. 2345 + 1587 → 2300 + 1600 = 3900
Roman Numerals:
1. 78 = LXXVIII
2. 56 = LVI
3. 99 = XCIX
Solve:
1. 6 stands for thousands in 56,739.
2. Smallest number: 1247
3. Rounded off: 540
Number Formation:
- Greatest number: 6531
- Smallest number: 1356

Chapter 1: Shapes and Space