Expanded Form

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

The 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.

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)

Place Value table

The following table shows the place value for the different digits,

How to Write 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: Get the standard form of the number.

Step 2: Identify the Place Values for each digits.

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 3: Multiply the place values with their respective digits

(6×1000), (4×100), (2×10), (7×1)

Step 4: Represent all the numbers as the sum of the product of the digit and their place value (digit × place value).

(6×1000) + (4×100) + (2×10) + (7×1)

Step 5: Represent the number in the Expanded Form

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

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.

3×1 + 6×0.1 + 9×0.01 + 2 ×0.001

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

3 + 0.6 + 0.09 + 0.002

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

3+0.6+0.09+0.002 = 3.692

Read More,

• Number System
• Rational Numbers

Solved Examples on 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.

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.

Conclusion

The expanded form of numbers in mathematics is a helpful way to break down large numbers into simpler parts. It shows the value of each digit based on its place in the number, making it easier to understand and work with. Whether you're adding, subtracting, or just learning about place value, using expanded form can make these tasks clearer and more manageable.