3-Digit Numbers
3-digit numbers are numbers that have three digits — a hundreds digit, a tens digit, and a ones digit. They range from 100 (the smallest 3-digit number) to 999 (the largest 3-digit number).
In Class 3, students learn to read, write, compare, and form 3-digit numbers. Understanding these numbers builds the foundation for working with larger numbers and performing addition, subtraction, and multiplication.
What is 3-Digit Numbers - Class 3 Maths (Numbers up to 1000)?
A 3-digit number is any number that has exactly three digits. The first digit (from the left) is in the hundreds place, the second digit is in the tens place, and the third digit is in the ones place.
The smallest 3-digit number is 100 and the largest 3-digit number is 999. There are 900 three-digit numbers in total (from 100 to 999).
| Hundreds | Tens | Ones | Number |
|---|---|---|---|
| 3 | 5 | 7 | 357 |
| 8 | 0 | 4 | 804 |
| 1 | 0 | 0 | 100 |
| 9 | 9 | 9 | 999 |
3-Digit Numbers Formula
How to form a 3-digit number:
Number = (Hundreds digit × 100) + (Tens digit × 10) + (Ones digit × 1)
For example, the number 572 is formed as: 5 × 100 + 7 × 10 + 2 × 1 = 500 + 70 + 2 = 572.
Rules for 3-digit numbers:
- The hundreds digit must be from 1 to 9 (never 0).
- The tens digit can be from 0 to 9.
- The ones digit can be from 0 to 9.
- Total 3-digit numbers = 9 × 10 × 10 = 900.
Successor and Predecessor:
- The successor of a number is the number that comes just after it. Successor of 456 = 457.
- The predecessor of a number is the number that comes just before it. Predecessor of 456 = 455.
- The successor of 999 is 1000 (a 4-digit number).
- The predecessor of 100 is 99 (a 2-digit number).
Types and Properties
Types of 3-digit numbers based on their digits:
- Numbers with all different digits: 357, 486, 921 — each digit is unique.
- Numbers with repeated digits: 334, 772, 551 — at least two digits are the same.
- Numbers with a zero in the tens or ones place: 305, 410, 600 — the zero holds the place.
Important: The hundreds digit of a 3-digit number can never be 0. If the hundreds digit were 0, the number would become a 2-digit number (e.g., 045 is just 45).
Solved Examples
Example 1: Reading a 3-Digit Number
Question: What number is shown? Hundreds = 4, Tens = 6, Ones = 2
Think:
- 4 hundreds = 400
- 6 tens = 60
- 2 ones = 2
- 400 + 60 + 2 = 462
Answer: The number is 462 (four hundred sixty-two).
Example 2: Identifying the Place of a Digit
Question: In the number 738, what is the place value of 3?
Think:
- 7 is in the hundreds place
- 3 is in the tens place
- 8 is in the ones place
- The digit 3 is in the tens place, so its value is 3 × 10 = 30
Answer: The place value of 3 in 738 is 30.
Example 3: Smallest and Largest 3-Digit Number from Given Digits
Question: Using digits 5, 2, and 8, form the smallest and largest 3-digit numbers.
Think:
- Arrange digits in ascending order: 2, 5, 8 → Smallest number = 258
- Arrange digits in descending order: 8, 5, 2 → Largest number = 852
Answer: Smallest = 258, Largest = 852.
Example 4: Forming Numbers with a Zero
Question: Using digits 0, 3, and 7, form the smallest 3-digit number.
Think:
- Ascending order of digits: 0, 3, 7
- But a 3-digit number cannot start with 0
- So the smallest digit (other than 0) goes first → 3
- Remaining digits in ascending order: 0, 7
- Smallest 3-digit number = 307
Answer: The smallest 3-digit number is 307.
Example 5: Word Problem — How Many Stickers?
Question: Aman has 3 hundred stickers, 4 tens of stickers, and 5 single stickers. How many stickers does Aman have?
Think:
- 3 hundreds = 300
- 4 tens = 40
- 5 ones = 5
- 300 + 40 + 5 = 345
Answer: Aman has 345 stickers.
Example 6: Finding Successor and Predecessor
Question: Write the number that comes just before and just after 500.
Think:
- Just before 500 → 500 − 1 = 499 (predecessor)
- Just after 500 → 500 + 1 = 501 (successor)
Answer: Predecessor = 499, Successor = 501.
Example 7: Counting 3-Digit Numbers with a Given Digit
Question: How many 3-digit numbers have 5 in the hundreds place?
Think:
- Hundreds place is fixed at 5 → numbers from 500 to 599
- Tens place can be 0 to 9 → 10 choices
- Ones place can be 0 to 9 → 10 choices
- Total = 10 × 10 = 100
Answer: There are 100 such 3-digit numbers (500 to 599).
Example 8: Even and Odd 3-Digit Numbers
Question: Is 746 an even number or an odd number?
Think:
- Check the ones digit → 6
- 6 is an even number (0, 2, 4, 6, 8 are even)
- So 746 is even
Answer: 746 is an even number.
Example 9: Word Problem — Auto-rickshaw Fare
Question: Priya reads the auto-rickshaw meter. It shows the fare as a 3-digit number. The hundreds digit is 1, the tens digit is double the hundreds digit, and the ones digit is 5. What is the fare?
Think:
- Hundreds digit = 1
- Tens digit = double of 1 = 2
- Ones digit = 5
- The number = 125
Answer: The fare is ₹125.
Example 10: Comparing Two 3-Digit Numbers
Question: Which is greater: 489 or 498?
Think:
- Hundreds digit: 4 = 4 (same)
- Tens digit: 8 vs 9 → 9 is greater
- So 498 > 489
Answer: 498 is greater than 489.
Real-World Applications
Where do we use 3-digit numbers?
- Money: Prices of many items are 3-digit numbers. A school bag may cost ₹450, a pair of shoes ₹750. When Ria goes shopping with her mother, she reads price tags that show 3-digit numbers.
- Distance: The distance between two cities is often a 3-digit number. Mumbai to Pune is about 150 km. Kavi's family drove 283 km to reach their grandparents' house.
- Weight: A packet of rice may weigh 500 g. Meera's school bag weighs about 350 g. Doctors measure weight in grams — many items weigh between 100 g and 999 g.
- Page numbers: Thick books have pages numbered in the hundreds. Aman's science textbook has 248 pages.
- Scores: In cricket, teams often score between 100 and 999 runs. India scored 356 runs in the first innings.
- Population: A small village may have a population in the hundreds. Priya's village has about 820 people.
Every time you count beyond 99 and before reaching 1000, you are working with 3-digit numbers. Learning to read, write, and understand these numbers is essential for daily life.
Key Points to Remember
- 3-digit numbers range from 100 (smallest) to 999 (largest).
- There are 900 three-digit numbers in total.
- A 3-digit number has three places: hundreds, tens, and ones.
- The hundreds digit is always 1 to 9 (never 0).
- The tens and ones digits can be 0 to 9.
- When forming the smallest number with a 0, place 0 in the tens or ones position, not the hundreds.
- The successor of 999 is 1000, which is a 4-digit number.
- The predecessor of 100 is 99, which is a 2-digit number.
Practice Problems
- Write the number name for 856.
- What is the place value of 7 in the number 271?
- Form the smallest 3-digit number using digits 9, 1, and 0.
- Write all 3-digit numbers that can be formed using digits 4, 0, and 5 (without repeating digits).
- Meera has 6 hundreds, 0 tens, and 3 ones. What number does she have?
- Which is the largest 3-digit even number?
- What comes just after 799?
- How many 3-digit numbers have all three digits the same?
Frequently Asked Questions
Q1. What is the smallest 3-digit number?
The smallest 3-digit number is 100. It has 1 in the hundreds place, 0 in the tens place, and 0 in the ones place.
Q2. What is the largest 3-digit number?
The largest 3-digit number is 999. It has 9 in every place — hundreds, tens, and ones.
Q3. How many 3-digit numbers are there?
There are 900 three-digit numbers, from 100 to 999. You can calculate this as 999 − 100 + 1 = 900.
Q4. Can a 3-digit number start with 0?
No. If a number starts with 0, it becomes a 2-digit or 1-digit number. For example, 075 is just 75 (a 2-digit number).
Q5. What comes after 999?
The number after 999 is 1000, which is the smallest 4-digit number. So 999 is the last 3-digit number.
Q6. What is the difference between face value and place value?
Face value is the digit itself (e.g., the face value of 5 in 253 is 5). Place value depends on the position (e.g., the place value of 5 in 253 is 50 because it is in the tens place).
Q7. How do you compare two 3-digit numbers?
Compare the hundreds digit first. If they are equal, compare the tens digit. If those are also equal, compare the ones digit. The number with the larger digit at the first unequal place is greater.
Q8. What is the place value of 0 in 305?
The place value of 0 in 305 is 0. Zero in any place has a place value of 0, but it is important because it holds the tens place and keeps 3 in the hundreds place.
Q9. Is 3-digit numbers covered in NCERT Class 3 Maths?
Yes. 3-digit numbers are part of the Numbers up to 1000 chapter in the NCERT/CBSE Class 3 Maths curriculum.
