Maths

Ordering Numbers

Class 3 | Comparing and Arranging Numbers

🎯 Learning Objectives

Compare two numbers using > (greater than), < (less than), and = (equal to) symbols.
Compare 3-digit and 4-digit numbers by checking digits from left to right.
Arrange numbers in ascending order (smallest to largest).
Arrange numbers in descending order (largest to smallest).
Form the greatest and smallest numbers from a given set of digits.
Apply comparison skills to real-life situations like cricket scores, prices, and populations.
Understand the rule: a number with more digits is always greater.

📖 Introduction

In a cricket match, India scored 287 runs and Australia scored 264 runs. Which team scored more? To answer this, we need to compare the two numbers. Comparing and ordering numbers is something we do every day — checking prices at a shop, reading cricket scores, or finding which city has more people!

In this chapter, we will learn how to compare 3-digit and 4-digit numbers, arrange them from smallest to largest (ascending order) and largest to smallest (descending order), and even form the biggest and smallest numbers from given digits.

Understanding Comparison Symbols

We use three special symbols to compare numbers:

Symbol	Name	Meaning	Example
>	Greater than	The number on the left is bigger	56 > 34
<	Less than	The number on the left is smaller	23 < 45
=	Equal to	Both numbers are the same	50 = 50

🐊 The Crocodile Rule: Think of the > and < signs as a crocodile's mouth. The crocodile is greedy — its mouth always opens towards the bigger number! So 8 > 3 means the mouth opens towards 8 (the bigger number).

Image: The Crocodile Rule

Crocodile mouth showing greater than and less than symbols — mouth opens towards bigger number

Comparing 3-Digit Numbers

To compare two 3-digit numbers, we check the digits from left to right:

Step 1: Compare the hundreds digit first. The number with the bigger hundreds digit is greater.

Step 2: If the hundreds digits are the same, compare the tens digit.

Step 3: If the tens digits are also the same, compare the ones digit.

Example 1

Compare 547 and 382
Hundreds: 5 > 3 → So 547 > 382
(We don't need to check tens or ones because hundreds are already different.)

Example 2

Compare 463 and 489
Hundreds: 4 = 4 (same, move to tens)
Tens: 6 < 8 → So 463 < 489

Example 3

Compare 725 and 723
Hundreds: 7 = 7 (same)
Tens: 2 = 2 (same)
Ones: 5 > 3 → So 725 > 723

Comparing 4-Digit Numbers

For 4-digit numbers, we follow the same rule — compare from left to right:

Step 1: Compare the thousands digit first.

Step 2: If thousands are the same, compare hundreds.

Step 3: If hundreds are the same, compare tens.

Step 4: If tens are the same, compare ones.

Example 1

Compare 3,456 and 2,789
Thousands: 3 > 2 → So 3,456 > 2,789

Example 2

Compare 5,230 and 5,280
Thousands: 5 = 5 (same)
Hundreds: 2 = 2 (same)
Tens: 3 < 8 → So 5,230 < 5,280

💡 Quick Rule: A 4-digit number is ALWAYS greater than a 3-digit number. For example, 1,000 > 999. The number with more digits wins!

Real-Life Example

Cricket Scores: In a match, India scored 3,245 runs in a series and England scored 3,198 runs. Who scored more?
Thousands: 3 = 3 (same)
Hundreds: 2 = 1? No! 2 > 1 → India scored more! 3,245 > 3,198

Ascending Order (Smallest to Largest)

When we arrange numbers from the smallest to the largest, it is called ascending order. Think of it as climbing up a staircase — each step is higher than the last.

We use the symbol < between numbers in ascending order.

Example 1

Arrange in ascending order: 456, 231, 789, 102
Compare all: 102 is smallest, then 231, then 456, then 789.
Answer: 102 < 231 < 456 < 789

Example 2

Arrange in ascending order: 2,450, 1,890, 3,100, 2,200
Compare thousands first: 1,890 (1 thousand) is smallest.
Then 2,200 and 2,450 (both 2 thousand — compare hundreds: 2 < 4).
Then 3,100 is largest.
Answer: 1,890 < 2,200 < 2,450 < 3,100

Indian Context

Prices at a shop: A bicycle costs ₹3,500, a cricket bat costs ₹1,200, a football costs ₹850, and a badminton racket costs ₹2,100. Arrange the prices in ascending order.
Answer: ₹850 < ₹1,200 < ₹2,100 < ₹3,500

Descending Order (Largest to Smallest)

When we arrange numbers from the largest to the smallest, it is called descending order. Think of it as coming down a staircase — each step is lower than the last.

We use the symbol > between numbers in descending order.

Example 1

Arrange in descending order: 345, 678, 123, 890
Answer: 890 > 678 > 345 > 123

Example 2

Arrange in descending order: 4,500, 2,300, 6,100, 1,800
Answer: 6,100 > 4,500 > 2,300 > 1,800

Indian Context

City populations (in thousands): Jaipur has 3,046 thousand people, Lucknow has 2,817 thousand, Patna has 2,049 thousand, and Bhopal has 1,798 thousand. Arrange in descending order.
Answer: 3,046 > 2,817 > 2,049 > 1,798 (Jaipur > Lucknow > Patna > Bhopal)

Image: Ascending and Descending Order

Child arranging number cards in ascending and descending order

How to Compare Step by Step

Here is a simple method to compare any two numbers:

Step	What to Do	Example: 4,356 vs 4,329
1	Count the digits. More digits = greater number.	Both have 4 digits. Move to step 2.
2	Compare thousands place.	4 = 4. Move to step 3.
3	Compare hundreds place.	3 = 3. Move to step 4.
4	Compare tens place.	5 > 2. So 4,356 > 4,329 ✓

Forming the Greatest and Smallest Numbers

Given a set of digits, we can form the greatest and smallest possible numbers.

Rules for Forming the Greatest Number:

Arrange the digits from largest to smallest (left to right).

Rules for Forming the Smallest Number:

Arrange the digits from smallest to largest (left to right).

Special Rule: If one of the digits is 0, it cannot be the first digit (because a number doesn't start with 0). Put the next smallest digit first, then place 0 after it.

Example 1

Digits: 5, 3, 8
Greatest number: 8 > 5 > 3 → 853
Smallest number: 3 < 5 < 8 → 358

Example 2

Digits: 7, 0, 4
Greatest number: 7 > 4 > 0 → 740
Smallest number: Can't start with 0! Next smallest is 4. → 407

Example 3 (4 digits)

Digits: 6, 2, 9, 1
Greatest number: 9 > 6 > 2 > 1 → 9,621
Smallest number: 1 < 2 < 6 < 9 → 1,269

Example 4 (4 digits with 0)

Digits: 3, 0, 5, 0
Greatest number: 5 > 3 > 0 > 0 → 5,300
Smallest number: Can't start with 0! Next smallest is 3. → 3,005

Real-Life Comparisons (Indian Context)

Cricket

IPL Match Scores:
Chennai Super Kings scored 185 runs. Mumbai Indians scored 179 runs.
Compare: Hundreds same (1=1), Tens: 8 > 7 → 185 > 179. CSK wins!

Shopping

Comparing Prices:
Rani wants to buy the cheaper notebook. Shop A sells it for ₹45 and Shop B for ₹38.
Compare: Tens: 4 > 3 → 45 > 38. So Shop B is cheaper (₹38 < ₹45).

Geography

Heights of Mountains (in metres):
Nanda Devi: 7,816 m | Kangchenjunga: 8,586 m | K2: 8,611 m
Ascending order: 7,816 < 8,586 < 8,611
(Nanda Devi < Kangchenjunga < K2)

📝 Key Words

Word	Meaning
Compare	To find which number is greater, smaller, or equal
Greater than (>)	The number on the left is bigger than the number on the right
Less than (<)	The number on the left is smaller than the number on the right
Equal to (=)	Both numbers have the same value
Ascending order	Arranging numbers from smallest to largest
Descending order	Arranging numbers from largest to smallest
Digits	The symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 used to write numbers
Place value	The value of a digit based on its position (ones, tens, hundreds, thousands)

⭐ Key Points to Remember

A number with more digits is always greater (e.g., 1,000 > 999).
To compare numbers with the same number of digits, start from the leftmost digit and move right.
The crocodile mouth (> or <) always opens towards the bigger number.
Ascending order = smallest to largest (going up). Descending order = largest to smallest (going down).
To form the greatest number, arrange digits from largest to smallest.
To form the smallest number, arrange digits from smallest to largest. If 0 is a digit, it cannot come first.
Always compare place by place: Thousands → Hundreds → Tens → Ones.

Finished learning? Now test what you know!

🎯 Quick Quiz — Test Yourself!

Answer these questions right here. You get instant feedback — no paper needed!

Score: 0 / 8

1. Which is the largest number?

543 has the biggest hundreds digit (5), so it is the largest.

2. Which is the smallest number?

190 has the smallest hundreds digit (1), so it is the smallest.

3. Which sign means "greater than"?

The sign > means "greater than". The sign < means "less than".

4. Numbers arranged from smallest to largest are in:

Smallest to largest is ascending order. Largest to smallest is descending order.

5. Put the correct sign: 456 ___ 398 (type >, < or =)

456 is greater than 398, so 456 > 398.

6. Put the correct sign: 210 ___ 320 (type >, < or =)

210 is less than 320, so 210 < 320.

7. Which is the largest: 456, 789, 234, 567? (digits only)

789 has the biggest hundreds digit (7), so it is the largest.

8. Which is the smallest: 321, 231, 123, 312? (digits only)

123 has the smallest hundreds digit (1), so it is the smallest.

✏️ Practice Questions

A. Compare Using >, <, or = (Fill in the blank)

1. 456 465

2. 789 698

3. 1,234 1,234

4. 3,050 3,500

5. 999 1,001

6. 5,678 5,687

7. 2,400 2,400

8. 870 807

9. 4,999 5,000

10. 6,321 6,312

B. Arrange in Ascending Order (Smallest to Largest)

1. 345, 123, 567, 234

2. 890, 450, 670, 320

3. 1,500, 2,300, 1,200, 3,400

4. 4,050, 4,500, 4,005, 4,550

5. 999, 1,001, 998, 1,010

C. Arrange in Descending Order (Largest to Smallest)

1. 678, 234, 890, 456

2. 1,100, 3,300, 2,200, 4,400

3. 5,010, 5,100, 5,001, 5,110

4. 750, 507, 705, 570

5. 8,200, 2,800, 8,020, 2,080

D. Form the Greatest and Smallest Number from Given Digits

1. Digits: 4, 7, 2 → Greatest: Smallest:

2. Digits: 9, 0, 5 → Greatest: Smallest:

3. Digits: 6, 3, 8, 1 → Greatest: Smallest:

4. Digits: 5, 0, 2, 7 → Greatest: Smallest:

5. Digits: 1, 0, 0, 3 → Greatest: Smallest:

E. Word Problems

1. Arjun has ₹2,350 and Meena has ₹2,530. Who has more money? By how much?

2. In a cricket match, Team A scored 176 runs and Team B scored 167 runs. Which team scored more? Write using > or <.

3. The distances from Delhi to four cities are: Jaipur 281 km, Agra 206 km, Lucknow 556 km, Chandigarh 243 km. Arrange these distances in ascending order.

4. A school has 1,245 students. Another school has 1,254 students. Which school has more students?

5. Using the digits 8, 3, 0, 5, form the greatest and smallest 4-digit numbers. Find the difference between them.

🎨 Fun Activity: Number Card Game

What you need: 10 small cards numbered 0 to 9.

How to play:

1. Shuffle the cards and pick any 4 cards.

2. Write down the digits you picked: , , ,

3. Form the greatest 4-digit number:

4. Form the smallest 4-digit number:

5. Now pick 3 more sets of 4 cards. Write all four greatest numbers and arrange them in descending order!

Challenge: Can you find the difference between your greatest and smallest number?

Want to review the lesson again?

Mathematics

Ordering Numbers

Class 3 | CBSE / NCERT / ICSE

Name: Class: Date:

Comparison Symbols

We use three symbols to compare numbers: > (greater than), < (less than), and = (equal to). The crocodile's mouth always opens towards the bigger number!

Symbol	Name	Meaning	Example
>	Greater than	Left number is bigger	56 > 34
<	Less than	Left number is smaller	23 < 45
=	Equal to	Both are the same	50 = 50

Comparing 3-Digit Numbers

Compare from left to right: Hundreds → Tens → Ones

Example: Compare 463 and 489
Hundreds: 4 = 4 (same) → Tens: 6 < 8 → So 463 < 489

Comparing 4-Digit Numbers

Compare from left to right: Thousands → Hundreds → Tens → Ones

Rule: A 4-digit number is ALWAYS greater than a 3-digit number.

Example: Compare 5,230 and 5,280
Thousands: 5 = 5 → Hundreds: 2 = 2 → Tens: 3 < 8 → So 5,230 < 5,280

Ascending Order (Smallest to Largest)

Arrange numbers from smallest to largest. Use < between them.

Example: 456, 231, 789, 102 → 102 < 231 < 456 < 789

Indian Context: Prices — Bicycle ₹3,500, Bat ₹1,200, Football ₹850, Racket ₹2,100
Ascending: ₹850 < ₹1,200 < ₹2,100 < ₹3,500

Descending Order (Largest to Smallest)

Arrange numbers from largest to smallest. Use > between them.

Example: 345, 678, 123, 890 → 890 > 678 > 345 > 123

Forming Greatest and Smallest Numbers

Greatest: Arrange digits from largest to smallest.

Smallest: Arrange digits from smallest to largest. (If 0 is a digit, it cannot come first.)

Digits: 7, 0, 4 → Greatest: 740 | Smallest: 407 (0 can't be first)
Digits: 6, 2, 9, 1 → Greatest: 9,621 | Smallest: 1,269

Key Points:

More digits = greater number (1,000 > 999).
Compare from left: Thousands → Hundreds → Tens → Ones.
Crocodile mouth opens towards the bigger number.
Ascending = smallest to largest. Descending = largest to smallest.
Greatest number: digits largest to smallest. Smallest: digits smallest to largest (0 not first).

Ordering Numbers — Practice

Class 3 | Mathematics

A. Compare Using >, <, or =

1. 456 465

2. 789 698

3. 1,234 1,234

4. 3,050 3,500

5. 999 1,001

6. 5,678 5,687

7. 2,400 2,400

8. 870 807

9. 4,999 5,000

10. 6,321 6,312

B. Arrange in Ascending Order (Smallest to Largest)

1. 345, 123, 567, 234

2. 890, 450, 670, 320

3. 1,500, 2,300, 1,200, 3,400

4. 4,050, 4,500, 4,005, 4,550

5. 999, 1,001, 998, 1,010

C. Arrange in Descending Order (Largest to Smallest)

1. 678, 234, 890, 456

2. 1,100, 3,300, 2,200, 4,400

3. 5,010, 5,100, 5,001, 5,110

4. 750, 507, 705, 570

5. 8,200, 2,800, 8,020, 2,080

D. Form the Greatest and Smallest Number

1. Digits: 4, 7, 2 → Greatest: Smallest:

2. Digits: 9, 0, 5 → Greatest: Smallest:

3. Digits: 6, 3, 8, 1 → Greatest: Smallest:

4. Digits: 5, 0, 2, 7 → Greatest: Smallest:

5. Digits: 1, 0, 0, 3 → Greatest: Smallest:

E. Word Problems

1. Arjun has ₹2,350 and Meena has ₹2,530. Who has more money? By how much?

2. In a cricket match, Team A scored 176 runs and Team B scored 167 runs. Which team scored more? Write using > or <.

3. Distances from Delhi: Jaipur 281 km, Agra 206 km, Lucknow 556 km, Chandigarh 243 km. Arrange in ascending order.

4. A school has 1,245 students. Another has 1,254 students. Which school has more?

5. Using digits 8, 3, 0, 5 — form the greatest and smallest 4-digit numbers. Find the difference.

🎨 Activity: Number Card Game
Pick 4 cards (digits 0–9). Write the digits, then form the greatest and smallest 4-digit numbers.
Digits picked: , , ,
Greatest number: | Smallest number:
Difference:

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