Expanded Form

Expanded form is a mathematical term, that is used to expand or split a given value. Therefore, in the expanded form, a number is divided into its place values and then expanded to display the value of each digit.

Let’s use the number 8741 as an example. Here, an expanded form helps in our understanding of each digit’s place value. Let’s attempt to determine the extended form of the given number 8741. The expanded version of 8741 is 8000 + 700 + 40 + 1.

In this article, we will learn various concepts related to expanded form, examples of expanded form, and others in detail.

What is Expanded Form?

Expanded form can be defined as a method of separating expressions or numbers into their parts. It involves expressing an algebraic statement as the sum of its words or a number as the sum of its place values and distributing decimal numbers at their place digit. The exact process of “expanding” varies depending on whether algebraic expressions or numbers are involved. Therefore, In various terms, we will learn the expanded forms of numbers.

Number	Ten thousand	Thousands	Hundreds	Tens	Ones
11				10	1
293			200	90	3
4321		4000	300	20	1
66578	60000	6000	500	70	8

Learning Place Value of any number is an important parameters in expanding various numbers. So let’s learn about it in brief.

What is Place Value?

Place value refers to the value that a digit in a number represents based on where it falls in the number. Even, It finds out how much each digit gives to the number’s total value. Each position in a multi-digit integer corresponds to a power of 10. So, let’s see the place value of the given digit 4,873.

• 4 is in Thousands Place (4,000)
• 8 is in Hundreds Place (800)
• 7 is in Tens Place (70)
• 3 is in Unit’s Place (3)

Writing Numbers in Expanded Form

Expanded form expresses the each number of the given value into its own place values which are specifically based on its position or breakdowns of the number, So let’s see the given value 6,427 in the following steps:

Step 1: Identify the Place Values

The place values are starting with unit digits, tens, hundreds, thousands, and so on.

• 6 is in Thousands Place (6,000)
• 4 is in Hundreds Place (400)
• 2 is in Tens Place (20)
• 7 is in Unit’s Place (7)

Step 2: In Expanded Form

Adding the numbers after expressing each one in terms of its place value:

6,427 = (6×1000) + (4×100) + (2×10) + (7×1)

Step 3: Adding the Values

6,000 + 400 + 20 + 7 = 6,427

So, the expanded form of 6,427 is 6,000 + 400 + 20 + 7

Now let’s learn about expanded form of various types of numbers.

Expanded Form of Whole Numbers

You have to be familiar with the place value that each digit represents in order to understand the complete value of a number. The places were stated from right to left. In these numbers, the digits are in the thousands, hundreds, tens, and ones places.

Let’s see the expanded form of the given whole number in the following Steps.

For Example: Find expanded form of 4,321

Step 1: In the number 4,321, the digits are in the thousands, hundreds, tens, and ones places.

4 (Thousands) + 3 (Hundreds) + 2 (Tens) + 1 (Ones)

Step 2: Then, express each digit in terms of its place value and add them up.

4×1000 + 3×100 + 2×10 + 1

Step 3: After that, simplify it by performing the multiplications.

4000 + 300 + 20 + 1

Step 4: At last, the individual numbers are combined, to get the final expanded form.

4000 + 300 + 20 + 1 = 4,321

Number	Thousands	Hundreds	Tens	Ones
4,321	4	3	2	1

Expanded Form of Decimal Numbers

Expansion of decimal numbers follows the same pattern as expansion of whole numbers. Here, The places were stated from left to right. We expressed the decimal number in the expanded form by writing the sum of the value of each digit in the given number.

For Example: Find Expanded form of 3.692

Step 1: In the number 3.692, the digits are in the tenths, hundredths, thousandths, and ten-thousandths places.

3 (Whole Part) + 6 (Tenths) + 9 (Hundredths) + 2 (Thousandths).

Step 2: Then, express each digit after the decimal point in terms of its place value.

3 + 0.6 + 0.09 + 0.002

Step 3: At last, the individual numbers are combined, to get the final expanded form.

3+0.6+0.09+0.002 = 3.692

Number	Whole Part	Tenths	Hundredths	Thousandths
3.692	3	0.6	0.09	0.002

Expanded form of Algebraic Expression

Algebraic expressions in the expanded form are simplified and any coefficients are assigned to each term included in the bracket. we expressed the original expression into the equivalent of the sum.

For Example: Find Expanded form of 2(x + 4)

Step 1: We have the expression (x + 4) that will be multiplied by 2.

Step 2: Then, distribute the coefficient to each term inside the bracket.

2×x + 2×4

Step 3: After that, simplify it by performing the multiplications.

2x + 8

Step 4: At last, the values can’t be added together because one is coefficient and another is coefficient with variable, So the expression can be expanded by this:

2x + 8

Read More,

• Number System
• Rational Numbers

Practice Questions on Expanded Form

Q1: Expand it 5(x+2).

Q2: Write 78,902 in its expanded form.

Q3: Show 5,753 in expanded form.

Q4: Write 8 Ten Thousands + 4 Thousands + 7 Hundreds + 3 Tens + 9 Ones in standard form.

Examples of Expanded Form

Various examples of Expanded Form is,

Example 1: Find the expanded form of 45316

Solution:

45316 = 4(Ten Thousands)+5(Thousands)+3(Hundreds)+1(Tens)+6(Ones)

45316 = 4×10,000 + 5×1000 + 3×100 + 1×10 + 6×1

45316 = 40000 + 5000 + 300 + 10 + 6

Example 2: Write 672 in its expanded form.

Solution:

672 = 6(Hundreds) + 7(Tens) + 2(Ones)

672 = 6×100 + 7×10 + 2×1

672 = 600 + 70 + 2

Example 3: Write 24.623 in its expanded form.

Solution:

24.623 = 2 Tens + 4 Ones + 6 Tenths + 2 Hundredths + 3 Thousandths

24.623 = 20 + 4 + 0.6 + 0.02 + 0.003

Therefore expanded form of 24.623 is 20 + 4 + 0.6 + 0.02 + 0.003

Example 4: Write standard form of 3000 + 200 + 40 + 8.

Solution:

3000 + 200 + 40 + 8 = 3,248

Example 5: Write 54,679 in expanded form.

Solution:

54,679 = 5(Ten Thousands) + 4(Thousands) + 6(Hundreds) + 7(Tens) + 9(Ones)

54,679 = 5×10,000 + 4×1000 + 6×100 + 7×10 + 9×1

54,679 = 50,000 + 4,000 + 600 + 70 + 9

Therefore Expanded Form of 54,679 is 50,000+4,000+600+70+9.

Example 6: Write 23.723 in its expanded form.

Solution:

23.723 = 2 Tens + 3 Ones + 7 Tenths + 2 Hundredths + 3 Thousandths

23.723 = 20 + 3 + 0.7 + 0.02 + 0.003

Therefore the expanded form of 23.723 is 20 + 3 + 0.7 + 0.02 + 0.003.

Expanded Form-FAQs

What is Expanded Form in Maths?

Expanded Form is a way in which numbers are expanded into sum of its placed values. In expanded form of any number we first break the number on the basis of its place value and then represent it in the form of the of their sum.

What is 35713 in Expanded Form?

Expanded form of the number 35713 is 30,000 + 5000 + 700 + 10 + 3.

What is 62 in Expanded Form?

Expanded form of the number 62 is 60 + 2.

What is Expanded Form of 29.72?

Expanded form of decimal number 29.72 is 20 + 9 + 0.7 + 0.02.

What is Significance of Expanded Form?

Expanded form is an important concept in math because it enable us to easily find the place value of each digit in any number.