Making Numbers from Given Digits (Rules, Examples, Game & Worksheets)

Learn how to make numbers from given digits using simple rules and step-by-step methods. This lesson explains how to form the smallest and greatest numbers by arranging digits in ascending and descending order, with special tips for handling zero correctly.

Through clear examples and easy explanations, students will understand how digit placement affects number value and how to avoid common mistakes while forming numbers. The page also includes practice questions to help reinforce learning and improve problem-solving skills.

This topic is essential for building a strong foundation in number concepts and is ideal for primary and middle school students. Whether you're preparing for exams or just improving your math basics, this guide makes learning quick and easy.

We can make numbers from the given digits. Let us see the rules.

Rules for Forming Numbers:

I: Formation of Smallest Number Rule:

To get the smallest number, arrange the digits in ascending order from left to right.

Example:

Write the smallest number using the digits 5, 2, 9, 3 and 1.

Solution:

The smallest number is 12,359.

II: Formation of Greatest Number Rule:

To get the greatest number, arrange the digits in descending order from left to right.

Example:

1. Write the greatest number using the digits 7, 8, 6, 2 and 4.

Solution: 

The greatest number is 87,642.

2. Write the smallest number and the greatest number using the digits 4, 3, 3, 8 and 7.

Solution:

The smallest number is 33,478.

The greatest number is 87,433.

III: If zero is one of the digits while forming the smaller number:

Trick to Handle Zero:

If zero is one of the digits while forming the smaller number, it is written in place after the highest place.

Example:

Using the digits 7, 2, 3, 0 and 5, write the smallest number.

Solution: The smallest number is 20,357.

Building Numbers:

● Making the biggest number from the four digits: We find the biggest number by writing the digits in descending order (biggest to smallest).

For example:

Given digits 5 7 8 3        →      Biggest number is 8753

● Making the smallest number from the four digits: We find the smallest number by writing the digits in ascending order (smallest to biggest).

For example:

Given digits 4 6 2 9        →      Smallest number is 2469

Note: We cannot have numbers starting with zeros.

● For making smallest number: Place zero after the next smallest digit. 

For example:

Given digits 0 4 5 0        →      Smallest number is 4005

For making biggest number: Place zero after the digits in descending order. 

For example:

Given digits 0 4 5 0        →      Biggest number is 5400

Forming the Smallest and the Largest Numbers using the Given Digits:

When digits are not repeated:

• The smallest 4-digit number using the digits, 5, 4, 1, 8 can be formed by arranging the digits in ascending order, i.e., 1 < 4 < 5 < 8. Thus, the required number is 1458.
• The largest 4-digit number using the digits 9, 7, 1, 3 can be formed by arranging the digits in descending order, i.e., 9 > 7 > 3 > 1. Thus, the required number is 9731.

If one of the digits is zero as in 4,7,8, 0 then the largest number = 8740 and the smallest number = 4078 and not 0478. 0478 is, in fact, a 3-digit number.

Example:

Write the smallest number and the greatest number using the digits 4, 3, 3, 8 and 7.

Solution:

The smallest number is 33,478.

The greatest number is 87,433.

When digits are repeated:

1. Write the smallest 4-digit number using the digits1, 4 and 6. (Digits may be repeated). 

Solution: To write the smallest number, we arrange the digits in ascending order, i.e. 1,4. 6. Since we have to make the smallest 4-digit number using the 3 given digits, we repeat the smallest digit, ie. 1. Therefore, the required smallest number is 1146.

2. Write the greatest 4-digit number using the digits 5 and 7. The digits may be repeated.

Solution:

Arranging the digits in descending order, we have 7 > 5. Since we have to make the greatest 4-digit number using the two digits 5 and 7, we repeat the greater digit.

Therefore, the required greatest number is 7775.

PLAY Game Smallest vs Largest Number Challenge 

Worksheet Making the Numbers From Given Digits:

Questions and Answers on Making the Numbers From Given Digits:

I. Make 4 digit numbers using the given digits:

(i) 8, 2, 5, 4

(ii) 7, 1, 5, 0

(iii) 5, 7, 6, 3

(iv) 3, 5, 4, 2

(v) 9, 1, 8, 7

(vi) 6, 9, 7, 8

Answers:

I. (i) 8254

(ii) 7150

(iii) 5763

(iv) 3542

(v) 9187

(vi) 6978

II. Write the smallest and biggest 4 digit numbers:

(i) 4, 7, 2, 9

(ii) 3, 2, 4, 8

(iii) 1, 9, 7, 6

(iv) 6, 8, 5, 2

(v) 7, 0, 1, 8

(vi) 5, 9, 4, 2

(vii) 9, 7, 2, 3

(viii) 3, 5, 1, 8

(ix) 7, 6, 3, 4

(x) 2, 5, 8, 4

(xi) 4, 0, 6, 0

(xii) 7, 9, 3, 1

Answer:

II. (i) Smallest 4-digit number: 2479; Biggest 4-digit number: 9742

(ii) Smallest 4-digit number: 2348; Biggest 4-digit number: 8432

(iii) Smallest 4-digit number: 1679; Biggest 4-digit number: 9761

(iv) Smallest 4-digit number: 2568; Biggest 4-digit number: 8652

(v) Smallest 4-digit number: 1078; Biggest 4-digit number: 8710

(vi) Smallest 4-digit number: 2479; Biggest 4-digit number: 9742

(vii) Smallest 4-digit number: 2379; Biggest 4-digit number: 9732

(viii) Smallest 4-digit number: 1358; Biggest 4-digit number: 8531

(ix) Smallest 4-digit number: 3467; Biggest 4-digit number: 7643

(x) Smallest 4-digit number: 2458; Biggest 4-digit number: 8542

(xi) Smallest 4-digit number: 4006; Biggest 4-digit number: 6400

(xii) Smallest 4-digit number: 1379; Biggest 4-digit number: 9731

3rd Grade Math Lessons

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