Expanded Form

Expanded form is a representation of numbers with the place value of each digit. This helps to understand the place value of numbers. To learn the large numbers, the expanded form is important. Numbers can be expanded in decimal expansion form, exponential expansion form, etc. This article explains how to expand the numbers. 

Table of Contents

• What is an Expanded Form?
• How to Write Numbers in Expanded Form?
• Expanded Form with Decimals
• Examples of Expanded Form
• Conclusion
• FAQs on Expanded Form
  
  

What is an Expanded Form?

The expanded form is that the numbers are written as the sum of each digit multiplied by its place value. This shows the position and value of a digit. 

Example:

The number 3,513 in expanded form is:

How to Write Numbers in Expanded Form?

The following steps explain how to write numbers in expanded form.

• Step 1: Identify the place value of each digit in standard form. It depends on whether the number is Indian place value system or the International place value system.

• Step 2: Multiply each digit by its place value.

• Step 3: Write in the form of a sum of all values. 

• Step 4: Exclude the digit zero as it does not add any value.
  
  

Example:

Expanded Form with Decimals

The decimal numbers can also be represented in the expanded form. There are two parts in decimal numbers: one is the digits before the decimal point and the other is the digits after the decimal point. The decimal digits are written in the expanded form by multiplying each digit by the increasing exponent value of 1/10.

Example: 

Write 3907.839 in expanded form.

Solution:

Write the decimal number in the place value chart.

 

 

3907.839 = 3 x 1000 + 9 x 100 + 0 x 10 + 7 x 1 + 8 x (1/10) + 3 x (1/10)2 + 9 x (1/10)3

3907.839 = 3000 + 900 + 0 + 7 + (8/10) + (3/100) + (9/1000)

3907.839 = 3000 + 900 + 7 + 0.8 + 0.03 + 0.009

Examples of Expanded Form

Example 1: Write the expanded form of 2086.

Solution: The expanded form of 2086 is as follows:

2086 = 2 x 1000 + 0 x 100 + 8 x 10 + 6 x 1

2086 = 2000 + 0 + 80 + 6

Example 2: Write the expanded form of 5,67,82,908.

Solution: The expanded form of 5,67,82,908 is as follows:

5,67,82,908 = 5 x 1,00,00,000 + 6 x 10,00,000 + 7 x 1,00,000 + 8 x 10,000 + 2 x 1,000 + 9 x 100 + 0 x 10 + 8 x 1

 5,67,82,908 = 500,00,000 + 60,00,000 + 7,00,000 + 80,000 + 2,000 + 900 + 0 + 8 

Conclusion

Expanded form makes it easier to understand the value of each digit in a number by breaking it down according to place value. The numbers, like whole numbers, decimal numbers, can be written in expanded form, which helps to improve the concept of place value and number sense. It is a foundational skill in mathematics that supports further learning in arithmetic, algebra, and beyond.

FAQs on Expanded Form

Q1. What is the expanded form of numbers?

Answer: The numbers in the form of the sum of each digit multiplied by its place value are known as the expanded form. 

Q2. What is the expanded form of 3458?

Answer: The expanded form of 3458 is as follows:

3458 = 3 x 1000 + 4 x 100 + 5 x 10 + 8 x 1

3458 = 3000 + 400 + 50 + 8

Q3. What Is the Difference Between Expanded Form and Standard Form?

Answer: The standard form is writing all digits together that form a number. The expanded form is written in the form of the sum of each digit multiplied by its place value.

Q4. What Is Expanded Form in Decimals?

Answer: The expanded form of decimals is that each of the decimal digits is written as an exponent of one-tenth.

Q5. Why Do We Need Expanded Form?

Answer: The value of each digit based on its place value can be understood from the expanded form. Thus, the expanded form is necessary for exploring numbers.