Expanded Form and Short Form of Numbers (With Examples, Video & Worksheet)

When we write a number as a sum of place value of its digits, the number is said to be in expanded form and when we write a number using digits, the number is said to be in short form. 

Understanding the expanded form and short form of a number is an essential concept in basic mathematics. It helps students learn how numbers are built using place values such as thousands, hundreds, tens, and ones.

In expanded form, a number is written as the sum of each digit multiplied by its place value. For example, 3,476 can be written as 3,000 + 400 + 70 + 6. This method makes it easier to understand the value of each digit in a number.

In short form (standard form), the number is written in its usual way using digits, such as 3476. Converting between expanded form and standard form helps improve number sense and strengthens foundational math skills.

This page includes:

• Clear explanations of expanded and short form
• Step-by-step examples
• Practice questions and worksheets
• Easy methods to convert numbers

By learning expanded notation and standard form of numbers, students can better understand place value and solve math problems more confidently.

What is Expanded Form?

When we write 3476, the number really means 3000 + 400 + 70 + 6. This means we have expanded the number to show the value of each of its digit.

The expanded form of a number is the method of expressing the number as the sum of the place value of all its digits.

For example,

Consider the number 2815

2815 = 2000 + 800 + 10 + 5

3476 = 3000 + 400 + 70 + 6

Expanded Form of a Number Video 📹 

Definition of Expanded Form of a Number:

Expanded form is writing a number as the sum of the place values of its digits. 

or, 

To express a number as the sum of the place values of its digits is called expanded form. 

Example:

Consider the numbers: (i) 3476; (ii) 6492; (iii) 9845

(i) 3476 = 3000 + 400 + 70 + 6.

(ii) 

There are 3 ways to write the expanded form for a given number.

Examples on Expanded Form of a Number:

1. Write the expanded form for 43,257.

Solution:

1^st way: 4 ten thousands + 3 thousands + 2 hundreds + 5 tens + 7 ones

2^nd way: 4 × 10000 + 3 × 1000 + 2 × 100 + 5 × 10 + 7 × 1

3^rd way: 40000 + 3000 + 200 + 50 + 7

2. Write the expanded form for 14,080.

Solution:

14,080 = 1 ten thousand + 4 thousands + 8 tens   [Note: We do not write the place value for hundreds and ones as these places are filled with zero.]

or, 1 × 10000 + 4 × 1000 + 8 × 10

or, 10000 + 4000 + 80

3. Write the expanded form of 6875.

Solution:

Expanded Form = 6 thousands + 8 hundreds + 7 tens + 5 ones

                       = 6000 + 800 + 70 + 5

What is Short Form (Standard Form)?

The standard form of a number is a way of expressing the expanded form in figures.

For example, the standard form of 7000 + 400 + 10 + 1 = 7411

Short Form of a Number Video 📹

Examples on Expanded Form and Short Form of a Number:

3. Write the short form for the given expanded forms.

(i) 8 ten thousands + 6 hundreds + 6 tens + 3 ones

(ii) 9  × 10000 + 7 × 1000 + 4 × 10 + 2

(iii) 40000 + 3000 + 900 + 70 + 8

Solution:

4. Write the following in short form:

(a) 7000 + 400 + 5

= 7 × 1000 + 4 × 100 + 0 × 10 + 5 × 1

= 7 thousands + 4 hundreds + 0 tens + 5 ones

= 7405

(b) 8000 + 600 + 90 + 6

= 8 × 1000 + 6 × 100 + 9 × 10 + 6 × 1

= 8 thousands + 6 hundreds + 9 tens + 6 ones

= 8696

Practice Quiz on Expanded Form and Standard Form

Worksheet on Expanded Form and Short Form of a Number:

Questions and Answers on Expanded Form and Standard Form of a Number:

I. Write in the expanded form:

(i) 5896

(ii) 3817

(iii) 6399

(iv) 1357

(v) 3434

(vi) 5690

Answer:

I. (i) 5000 + 800 + 90 + 6

(ii) 3000 + 800 + 10 + 7

(iii) 6000 + 300 + 90 + 9

(iv) 1000 + 300 + 50 + 7

(v) 3000 + 400 + 30 + 4

(vi) 5000 + 600 + 90 + 0

II. Write the expanded form:

(i) 4718 = ____ + ___ + __ + _

(ii) 7098 = ____ + ___ + __ + _

(iii) 5002 =  ____ + ___ + __ + _

(iv) 6500 = ____ + ___ + __ + _

(v) 3456 =  ____ + ___ + __ + _

Answer:

II. (i) 4718 = 4000 + 700 + 10 + 8

(ii) 7098 = 7000 + 000 + 90 + 8

(iii) 5002 =  5000 + 000 + 00 + 2

(iv) 6500 = 6000 + 500 + 00 + 0

(v) 3456 =  3000 + 400 + 50 + 6

III. Write in the standard form:

(i) 2000 + 900 + 90 + 9

(ii) 8000 + 200 + 50 + 3

(iii) 1000 + 400 + 50 + 2

(iv) 4000 + 300 + 9

(v) 6000 + 900 + 80 + 4

Answer:

III. (i) 2999

(ii) 8253

(iii) 1452

(iv) 4309

(v) 6984

IV. Write in the short form:

(i) 3000 + 60

(ii) 7000 + 70 + 8

(iii) 8000 + 80 + 9

(iv) 4000 + 500 + 10 + 3

(v) 6000 + 900 + 70

Answer:

IV. Write in the short form:

(i) 3060 

(ii) 7078

(iii) 8089

(iv) 4513

(v) 6970

V. Complete the puzzle with answers in short form. Clues have been given below.

Answer:

V. 

Short Form of International Number System

VI. Express in short form.

(i) 10,000,000,000 + 2,000,000,000 + 50,000,000 + 5,000,000 +  5,000 + 200 + 40 + 5

(ii) 50,00,00,000 + 3,00,00,000 + 40,00,000 + 5,00,000 + 30,000 + 5,000 + 800 + 50 + 8

(iii) 6,00,00,000 + 20,00,000 + 5,00,000 + 20,,000 + 2000 + 400 + 10 + 2

(iv) 100,000,000,000 + 10,000,000,000 + 2,000,000,000 + 400,000,000,000 + 20,000,000 + 5,000,000 + 100,000 + 20,000 + 4,000 + 300 + 40 + 6

Answer:

VI. (i) 12,555,005,245

(ii) 53,45,35,858

(iii) 6,25,22,412

(iv) 112,425,124,346

3rd Grade Math Lessons

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