4-Digit Numbers
A 4-digit number is any number from 1000 to 9999. These numbers use four places: Thousands, Hundreds, Tens, and Ones.
The smallest 4-digit number is 1000 (one thousand) and the largest is 9999 (nine thousand nine hundred ninety-nine). There are 9000 four-digit numbers in all (9999 − 1000 + 1 = 9000).
Understanding 4-digit numbers is the foundation for working with larger numbers, performing addition and subtraction with regrouping, and reading real-life quantities like distances, prices, and populations.
What is 4-Digit Numbers - Class 4 Maths (Large Numbers)?
A 4-digit number is a number that has exactly four digits. The first digit (from the left) is in the thousands place and cannot be 0. The remaining three digits occupy the hundreds, tens, and ones places and can be any digit from 0 to 9.
General form: A 4-digit number can be written as ABCD, where A is 1–9 and B, C, D are 0–9.
| Thousands (Th) | Hundreds (H) | Tens (T) | Ones (O) |
|---|---|---|---|
| 1–9 | 0–9 | 0–9 | 0–9 |
4-Digit Numbers Formula
4-digit number = Thousands × 1000 + Hundreds × 100 + Tens × 10 + Ones × 1
Key facts:
- Smallest 4-digit number = 1000
- Largest 4-digit number = 9999
- Total 4-digit numbers = 9000
- 1000 comes just after the 3-digit number 999
- 9999 comes just before the 5-digit number 10000
Types and Properties
Reading 4-digit numbers:
- 3526 → Three thousand five hundred twenty-six
- 7040 → Seven thousand forty
- 1009 → One thousand nine
- 5800 → Five thousand eight hundred
Writing number names as numerals:
- Four thousand three hundred sixty-one → 4361
- Eight thousand seven → 8007
- Six thousand nine hundred → 6900
Place value breakdown:
In the number 4738:
| Digit | Place | Place Value |
|---|---|---|
| 4 | Thousands | 4 × 1000 = 4000 |
| 7 | Hundreds | 7 × 100 = 700 |
| 3 | Tens | 3 × 10 = 30 |
| 8 | Ones | 8 × 1 = 8 |
So, 4738 = 4000 + 700 + 30 + 8.
Solved Examples
Example 1: Example 1: Identifying a 4-digit number
Problem: Which of these are 4-digit numbers: 987, 1005, 10234, 6000, 0452?
Solution:
Step 1: Count the digits in each number.
- 987 → 3 digits (not 4-digit)
- 1005 → 4 digits (4-digit number)
- 10234 → 5 digits (not 4-digit)
- 6000 → 4 digits (4-digit number)
- 0452 → starts with 0, so it is actually 452, a 3-digit number
Answer: 1005 and 6000 are 4-digit numbers.
Example 2: Example 2: Writing a number in words
Problem: Write 3079 in words.
Solution:
Step 1: Break the number by place value: 3 thousands, 0 hundreds, 7 tens, 9 ones.
Step 2: Read: Three thousand seventy-nine.
(Note: We skip saying "zero hundred.")
Answer: Three thousand seventy-nine
Example 3: Example 3: Writing numeral from words
Problem: Write the numeral for "Six thousand four hundred five."
Solution:
Step 1: Six thousand = 6000
Step 2: Four hundred = 400
Step 3: Five = 5
Step 4: No tens mentioned, so tens digit is 0.
Answer: 6405
Example 4: Example 4: Finding the place value of a digit
Problem: What is the place value of 5 in 2563?
Solution:
Step 1: Write the place value chart:
| Th | H | T | O |
|---|---|---|---|
| 2 | 5 | 6 | 3 |
Step 2: 5 is in the hundreds place.
Step 3: Place value = 5 × 100 = 500.
Answer: The place value of 5 in 2563 is 500.
Example 5: Example 5: Predecessor and successor
Problem: Find the predecessor and successor of 4000.
Solution:
Step 1: Predecessor = 4000 − 1 = 3999
Step 2: Successor = 4000 + 1 = 4001
Answer: Predecessor = 3999, Successor = 4001
Example 6: Example 6: Word problem – reading bus numbers
Problem: Aman's school bus has the number 4718. Write this number in expanded form and in words.
Solution:
Step 1: Expanded form: 4000 + 700 + 10 + 8
Step 2: In words: Four thousand seven hundred eighteen
Answer: 4718 = 4000 + 700 + 10 + 8 = Four thousand seven hundred eighteen
Example 7: Example 7: Forming the smallest and largest number
Problem: Using digits 3, 0, 7, 5 (each once), form the smallest and largest 4-digit numbers.
Solution:
Largest number: Arrange digits in descending order → 7, 5, 3, 0 → 7530
Smallest number: Arrange in ascending order → 0, 3, 5, 7. But 0 cannot be the first digit. So swap 0 and 3 → 3057
Answer: Largest = 7530, Smallest = 3057
Example 8: Example 8: Even and odd 4-digit numbers
Problem: Is 8246 even or odd? What about 5173?
Solution:
Step 1: Look at the ones digit of each number.
- 8246 → ones digit is 6 (even) → 8246 is even
- 5173 → ones digit is 3 (odd) → 5173 is odd
Answer: 8246 is even; 5173 is odd.
Example 9: Example 9: Word problem – cost of items
Problem: Priya bought a bicycle for ₹3450 and a helmet for ₹1250. What is the total cost?
Solution:
Step 1: Total cost = ₹3450 + ₹1250
Step 2: Add ones: 0 + 0 = 0
Step 3: Add tens: 5 + 5 = 10 (write 0, carry 1)
Step 4: Add hundreds: 4 + 2 + 1 = 7
Step 5: Add thousands: 3 + 1 = 4
Answer: Total cost = ₹4700
Example 10: Example 10: Counting 4-digit numbers with conditions
Problem: How many 4-digit numbers have 5 in the thousands place?
Solution:
Step 1: Thousands digit is fixed as 5.
Step 2: Hundreds digit can be 0–9 → 10 choices
Step 3: Tens digit can be 0–9 → 10 choices
Step 4: Ones digit can be 0–9 → 10 choices
Step 5: Total = 10 × 10 × 10 = 1000
Answer: There are 1000 four-digit numbers with 5 in the thousands place (5000 to 5999).
Key Points to Remember
- A 4-digit number ranges from 1000 to 9999.
- The four places are: Thousands, Hundreds, Tens, Ones (left to right).
- The thousands digit is always 1 to 9 (never 0).
- The smallest 4-digit number is 1000; the largest is 9999.
- There are exactly 9000 four-digit numbers.
- 999 + 1 = 1000 (the bridge from 3-digit to 4-digit numbers).
- Each digit's place value depends on its position: thousands = × 1000, hundreds = × 100, tens = × 10, ones = × 1.
- When forming the smallest number with a 0, place 0 in the second position (not the first).
Practice Problems
- Write the number name for 7206.
- Write the numeral for "Five thousand ninety."
- What is the place value of 8 in 8041?
- Find the predecessor and successor of 6999.
- Using digits 2, 8, 0, 4, form the largest and smallest 4-digit numbers (use each digit once).
- How many 4-digit numbers are there between 3000 and 4000 (not including 3000 and 4000)?
- Kavi bought a table for ₹2375 and a chair for ₹1420. What is the total amount?
- Arrange in ascending order: 4502, 4052, 4520, 4205.
Frequently Asked Questions
Q1. What is the smallest 4-digit number?
The smallest 4-digit number is 1000 (one thousand). It comes right after the largest 3-digit number, 999.
Q2. What is the largest 4-digit number?
The largest 4-digit number is 9999 (nine thousand nine hundred ninety-nine). Adding 1 to it gives 10000, which is a 5-digit number.
Q3. How many 4-digit numbers are there in total?
There are 9000 four-digit numbers. They range from 1000 to 9999, so 9999 − 1000 + 1 = 9000.
Q4. Can a 4-digit number start with 0?
No. If the first digit is 0, the number becomes a 3-digit (or smaller) number. For example, 0453 is just 453, a 3-digit number.
Q5. What is the difference between face value and place value?
Face value is the digit itself regardless of position. Place value depends on the position. In 4738, the face value of 7 is 7, but its place value is 700 because it is in the hundreds place.
Q6. How do you read a 4-digit number with zeros?
Skip the place name when the digit is 0. For example, 3007 is read as "three thousand seven" — you do not say "zero hundred" or "zero ten."
Q7. What comes after 9999?
10000 (ten thousand), which is the smallest 5-digit number.
Q8. How do you form the smallest 4-digit number from given digits?
Arrange the digits in ascending order. If 0 is among them, place the next smallest non-zero digit first, then 0, followed by the rest. For example, from 5, 0, 3, 1 → smallest is 1035.
Q9. Is 4-digit numbers covered in NCERT Class 4 Maths?
Yes. The NCERT Class 4 textbook (Math Magic) covers 4-digit numbers in the chapter on large numbers, including reading, writing, comparing, and operations on these numbers.
Related Topics
- Place Value of 4-Digit Numbers
- Numbers up to 1000
- Expanded Form of 4-Digit Numbers
- 5-Digit Numbers
- Place Value of 5-Digit Numbers
- Comparing Large Numbers (Grade 4)
- Ordering Large Numbers (Grade 4)
- Rounding Numbers (Grade 4)
- Estimation (Grade 4)
- Roman Numerals (I to C)
- Numbers up to 1,00,000
- Predecessor and Successor (Grade 4)
