Expanded Form: Definitions, Examples, Factor Form, Decimal Form, Exponential Form, Calculator, and Benefits

Expanded Form Overview

The value of each digit of a number can be written in expanded form in mathematics. The expanded version of the numbers are the numbers that are represented as the sum of each digit multiplied by its place value. We will go through the expanded form of a number, the expanded form of decimal numbers, the expanded factor form, and the expanded exponential form in-depth, with many sample questions.

What is Expanded Form?

The process of breaking down or splitting integers into their right place value is known as expanded form. It is frequently used to perform huge sums in the absence of a calculator. It can also help us comprehend the distinction between thousands, hundreds, tenths, single units, and decimal places.

Examples of Expanded Form

For example: Consider the number 987654321.. This statistic is difficult to fathom. In this situation, an enlarged form helps us grasp each number depending on its place value. The number 987654321 may also be written as-

900000000 + 80000000 + 7000000 + 600000 + 50000 + 4000 + 300 + 20 + 1

The number has been enlarged to show the value of each digit.  

Expanded Form in Numbers

The extended form of the numbers aids in determining the position of each digit in the provided number. It signifies that number growth is dependent on place value. The enlarged form divides the number into units, tens, hundreds, and thousands. The extended version of the number 1572, for example, is 1000+500+70+2.

Some instances of extended forms of numerals are shown in the table below-

Consider the number 123. There are 1 hundreds, 2 tens, and 3 ones in the number 123.

More Expanded Form Examples

The following are some more examples of Expanded Forms- 

1. 67+0 is the enlarged version of 67. There are six tens and seven ones in the number 67.
2. The extended version of 280 is 200+80+0 because there are no ones.
3. 20,000 has the extended form 20000+0+0+0+0. There are zero thousand, zero hundred, zero tens, and zero ones in the number 20,000.

Expanded Factor Form

The conventional form of the number is written in its expanded factor form. When a number is represented as the product of a digit and its place value, it is written in expanded factor form.

A sum of (Digit Place value + Expanded Factor Form).

Read more about the Place Value and Face Value and the Father of Mathematics.

How to Write Numbers in Expanded Form?

The following are some of the numbers in expanded form-

Step 1: Determine the number's standard form.

Step 2: Using the place value table, determine the place value of the provided integer.

Step 3: Multiply the provided digit by its place value and write the result as (digit place value).

Step 4: Finally, express all of the numbers as the sum of (digit place value) form, which is the number's expanded form.

Example: What is the extended form of 34287?

Solution-

Step 1: 34287 is the usual form of the number.

Step 2: The supplied number's place value is-

3 - Ten Thousand

4 - Thousands

2 - Hundreds

8 - Tens

7 - Ones

Step 3: Take the supplied integer and multiply it by its place value.

(i.e.,) 3×10, 000, 4×1000, 2×100, 8×10, 7×1

Step 4: 30,000 + 4000 + 200 + 80 + 7 is the expanded form.

Finally, 34287 has the enlarged form 30,000 + 4000 + 200 + 80 + 7.

How to Write Whole Numbers in Expanded Form?

The procedures for writing any whole number in expanded form are as follows-

1. Get the number in its simplest form.
2. Determine its place values using the place value chart.
3. Multiply the integer by its place value.
4. It will be shown as a digit place value.
5. The product of the digit and its place value should be used to represent all digits.

Expanded Form of Decimals Numbers

The extended form of decimal numerals can also be written. When expressing decimals in expanded form, we must multiply each decimal digit by an increasing exponent of 1/10. The digits following the decimal points are represented on the place value chart as tenths (1/10), hundredths (1/100), thousandths (1/1000), and so on.

Consider the following example: 59.30. 

1. First, write the number in its enlarged form before the decimal point. (i.e.) 59.
2. 50+9 is the extended version of 59.
3. The enlarged form 30 is now 3(1/10) + 0(1/100). [Because 3 is the tenth place and 0 is the hundredth position.]
4. As a result, the extended form of 59.30 is 50+9+(3/10)+(0/100).
5. The enlarged form above can alternatively be written as 50+9+0.3+0.00.

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Expanded Exponential Form

The place value of the digits is expressed in expanded exponential form by powers of 10. It implies that the number one is represented by 10⁰, the number ten is represented by 10¹, the number hundred is represented by 10², and so on. The extended exponential form of 8973, for example, is represented by-

8 – Thousands (8 ×10³)

9 – Hundreds (9 × 10²)

7 – Tens (7 × 10¹)

3 – Ones (3 × 10⁰)

As a result, the extended exponential form of 8973 is (8 ×10³) + (9 × 10²) + (7 × 10¹) + (3 × 10⁰).

Expanded Form Calculator

The rules of the extended form calculator are straightforward. All you have to do is take the following three simple steps-

1. Fill fill the "Number" field with the desired number in expanded notation.
2. To acquire the desired result, select the relevant term in "form": numbers, factors, or exponents.
3. Get the outcome.

Benefits of Learning Expanded Form

The following are some of the benefits of expanded form-

1. Large numbers can be broken down into smaller independent digits using Expanded Form. 
2. As a result, it facilitates complicated problem-solving in a more understandable manner.
3. Expanded Form can assist us in comprehending place value in the context of regular numbers.
4. As a useful tool for mental arithmetic, it may also assist us with simple math issues in everyday life without the need for a calculator. 
5. For example, we might use Expanded Form to calculate the total number of students in many classes or the quantity of ingredients for a dish.
6. This also teaches a significant level of mental discipline and logical thinking to frequent challenges within the context of Maths schooling. 
7. Overall, these skills can help students in other areas such as science and musical notation.

Practice Questions Related to Expanded Form

Solve the following questions-

Practice Question 1: In exponential form, expand the decimal value to 1.347.

Practice Question 2: In exponential form, expand the number 8709. 

Practice Question 3: Expand the number 58945.

Practice Question 4: Convert the extended form of the number 5.7987.

Practice Question 5: Expand the decimal number 38.095.