Forming Numbers Using Digits
Forming numbers using given digits is a key skill in Class 4 Maths. You learn to arrange digits to make the largest number, smallest number, or numbers that meet specific conditions.
This skill strengthens your understanding of place value. A digit's position decides its value — putting a large digit in the ten-thousands place makes the number much bigger than putting it in the ones place.
What is Forming Numbers Using Digits - Class 4 Maths (Large Numbers)?
Forming numbers means arranging a given set of digits in a specific order to create a numeral.
Largest number → Arrange digits in descending order
Smallest number → Arrange digits in ascending order
Special rule for 0: If 0 is one of the given digits, it cannot be placed in the leftmost position (a number cannot start with 0). Place the next smallest digit first, then 0.
Types and Properties
Types of number-forming problems:
- Largest number: Place the biggest digit at the highest place value.
- Smallest number: Place the smallest non-zero digit at the highest place value. If 0 is present, place it in the second position.
- Numbers with conditions: Form a number where a specific digit is in a specific place.
- Numbers with repetition: When a digit appears more than once.
Solved Examples
Example 1: Example 1: Largest 4-digit Number
Problem: Form the largest 4-digit number using the digits 3, 7, 1, 9.
Solution:
Step 1: Arrange digits in descending order: 9, 7, 3, 1
Step 2: Write the number: 9731
Answer: The largest number is 9,731.
Example 2: Example 2: Smallest 4-digit Number
Problem: Form the smallest 4-digit number using the digits 5, 2, 8, 4.
Solution:
Step 1: Arrange digits in ascending order: 2, 4, 5, 8
Step 2: Write the number: 2458
Answer: The smallest number is 2,458.
Example 3: Example 3: Smallest Number with 0
Problem: Form the smallest 4-digit number using the digits 6, 0, 3, 8.
Solution:
Step 1: Ascending order would give 0, 3, 6, 8 — but a number cannot start with 0.
Step 2: Place the next smallest digit (3) first, then 0, then the rest in ascending order.
Step 3: Number = 3,068
Answer: The smallest number is 3,068.
Example 4: Example 4: Largest 5-digit Number
Problem: Form the largest 5-digit number using the digits 4, 0, 7, 2, 9.
Solution:
Step 1: Arrange in descending order: 9, 7, 4, 2, 0
Answer: The largest number is 97,420.
Example 5: Example 5: Smallest 5-digit Number with 0
Problem: Form the smallest 5-digit number using the digits 5, 0, 1, 0, 3.
Solution:
Step 1: Ascending order: 0, 0, 1, 3, 5 — cannot start with 0.
Step 2: Place the smallest non-zero digit (1) first: 1, 0, 0, 3, 5
Answer: The smallest number is 10,035.
Example 6: Example 6: Using Repeated Digits
Problem: Form the largest number using the digits 5, 5, 3, 8.
Solution:
Step 1: Arrange in descending order: 8, 5, 5, 3
Answer: The largest number is 8,553.
Example 7: Example 7: Number with a Condition
Problem: Using digits 6, 2, 9, 4, form a 4-digit number where 9 is in the hundreds place.
Solution:
Step 1: Fix 9 in the hundreds place: _ 9 _ _
Step 2: To make the largest such number, put 6 in thousands, 4 in tens, 2 in ones: 6,942
Answer: One such number is 6,942.
Example 8: Example 8: Word Problem
Problem: Meera has 5 cards with digits 1, 3, 5, 7, 9. She wants to form the largest and smallest 5-digit numbers. Find both.
Solution:
Largest: Arrange in descending order → 97,531
Smallest: Arrange in ascending order → 13,579
Answer: Largest = 97,531, Smallest = 13,579.
Example 9: Example 9: Difference Between Largest and Smallest
Problem: Using the digits 2, 5, 0, 8, find the difference between the largest and smallest 4-digit numbers.
Solution:
Step 1: Largest number: 8,520
Step 2: Smallest number: 2,058 (0 cannot be first, so 2 goes first)
Step 3: Difference = 8,520 − 2,058 = 6,462
Answer: The difference is 6,462.
Example 10: Example 10: All Possible 2-digit Numbers
Problem: Using digits 3 and 7, how many 2-digit numbers can you form (without repeating)?
Solution:
The two possible numbers are: 37 and 73.
Answer: 2 numbers — 37 and 73.
Key Points to Remember
- To form the largest number, arrange digits in descending order (biggest first).
- To form the smallest number, arrange digits in ascending order (smallest first).
- If 0 is among the digits, it cannot be the first digit. Use the next smallest digit in the first position.
- The difference between the largest and smallest number formed from the same digits is always the same, regardless of order.
- A digit's position (place value) determines how much it contributes to the number.
- When digits repeat, treat each copy as a separate digit during arrangement.
Practice Problems
- Form the largest and smallest 4-digit numbers using 4, 1, 7, 3.
- Form the smallest 5-digit number using 9, 0, 2, 5, 0.
- Using the digits 6, 0, 8, 2, form a 4-digit number where 8 is in the tens place.
- Rahul has digit cards 3, 5, 7, 1, 9. What is the largest 5-digit number he can form?
- Find the difference between the largest and smallest 4-digit numbers using 6, 3, 0, 9.
- How many 3-digit numbers can you form using digits 1, 2, 3 (without repeating)?
- Form the smallest 4-digit number using 0, 0, 5, 1.
Frequently Asked Questions
Q1. How do you form the largest number from given digits?
Arrange all the given digits in descending order (from biggest to smallest). The digit with the highest value goes in the leftmost place. For example, digits 3, 7, 1 give 731.
Q2. What if 0 is one of the digits for the smallest number?
A number cannot start with 0. Place the smallest non-zero digit in the first position, then place 0 in the second position, followed by the remaining digits in ascending order.
Q3. Can you form a 4-digit number with only 3 different digits?
Yes, if repetition is allowed. For example, with digits 2, 5, 8 and repetition allowed, you can form 2,258 or 8,852. Without repetition, you cannot form a 4-digit number from 3 digits.
Q4. How many numbers can be formed from 4 digits without repetition?
With 4 distinct digits (none being 0), you can form 4 x 3 x 2 x 1 = 24 different 4-digit numbers. If one digit is 0, slightly fewer numbers are possible since 0 cannot lead.
Q5. Why does the position of a digit matter?
The position determines the place value. The digit 5 in the thousands place means 5,000, while 5 in the ones place means just 5. This is why placing larger digits in higher places creates larger numbers.
Q6. What is the difference between face value and place value when forming numbers?
Face value is the digit itself (always the same). Place value depends on position. When forming numbers, you use place value to decide where each digit should go to make the number largest or smallest.
Q7. How do you form numbers with repeated digits?
Treat each copy of the digit separately. For example, with digits 3, 3, 5, 7, the largest number is 7,533 and the smallest is 3,357.
Q8. Is forming numbers part of NCERT Class 4?
Yes, forming the largest and smallest numbers from given digits is a standard topic in CBSE/NCERT Class 4 Maths under the chapter on large numbers and place value.
Related Topics
- Place Value of 4-Digit Numbers
- Comparing Large Numbers (Grade 4)
- 4-Digit Numbers
- Expanded Form of 4-Digit Numbers
- 5-Digit Numbers
- Place Value of 5-Digit Numbers
- 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)
