Expanded Form and Short Form of a Number – Worksheets with Answer

Expanded Form and Short Form of a Number Definition with Examples

In Mathematics, the extended form assists us in better understanding a particular number. Take the number 985287841 as an example. Can you make sense of this number by taking a look at it? Obviously not! Therefore, an extended form of a number helps us understand the placement of each digit depending on its place value.

Let us look at the number 652 and see if we can identify its expanded form. The expanded form of 652 is 600 + 50 + 2. It signifies six hundreds, five tens, and two ones in this number. The expanded form of a number allows us to understand the significance of each digit quickly.

It is tough to understand a number with a large number of digits if you do not know how to represent it in expanded form. The extended form allows us to understand the components of big numbers.

Each number can get written in one of the following ways: 1, 10, 100, 1000. Let us now learn more about the expanded form, given that we have this understanding.

Expanded Form: Meaning

Any number can get broken down into a sum of whole numbers. In mathematics, each digit’s value can get expressed in expanded form. The expanded version of a number represents the sum of each digit multiplied by its place value.

Take an example of the expanded form,

1,628 = 1*1000 + 6*100 + 2*10 + 8*1.

Let us take another example – The figure 6426 really stands for 6000 + 400 + 20 + 6. It indicates the expanded form of the number to reveal the value of each of its digits. The extended form of a number represents it as the sum of all its digits’ place values.

Steps to write in expanded form:

The steps to writing the expanded form are as follows:

• Obtain the number in its most basic form.
• Using the place value chart, determine its place values.
• Place value multiplied by the number
• It should represent a digit place value.
• All digits should be presented as the digit’s product and place value.

Short Form

The figure that genuinely depicts the absolute number is known as the short form. We can also shorten any expanded number by simply adding the value of all digits based on their place value. Let us determine the short form of an expanded form – 400 + 60 + 3. 463 is the abbreviated version of the larger form, which comprises four hundreds, six tens, and four ones.

Let us take another example of the short form.

1,000 + 700 + 60 + 8 = 1768

Hence, 1768 is the short form.

Write these numbers in expanded/short form

1. Express in expanded form:

1. 7687
2. 6523
3. 9701
4. 1678
5. 7676
6. 4680

2. Express in standard form:

1. 7000 + 100 + 80 + 7
2. 3000 + 700 + 50 + 3
3. 4000 + 600 + 70 +8
4. 1000 + 500 + 10 + 2
5. 9000 + 300 + 1
6. 8000 + 400 + 20 + 5

Answers:

1.

1. 7000 + 600 + 80 + 7
2. 6000 + 500 + 20 + 3
3. 9000 + 700 + 1
4. 1000 + 600 + 70 + 8
5. 7000 + 600 + 70 + 6
6. 4000 + 600 + 80 + 0

2.

1. 7187
2. 3753
3. 4678
4. 1512
5. 9301
6. 8425

FAQs (Frequently Asked Questions)

Define expanded form and short form.

Expanded form: A number’s extended form represents it as the sum of all its digits’ place values.

Short form: The expanded form of a number expressed in figures is its short form.

How to write numbers in expanded form?

The separation of numbers depending on place values is known as number expansion. The expanded form aids us in understanding the place value of each digit in a number.

In addition, there are three methods to write numbers in expanded form.

The number 4537 can be written,

In one way of expanded form,

6537 = 6000 + 500 + 30 + 7,

In a second way,

6537 = 6 × 1000 + 5 × 100 + 3 × 10 + 7 × 1,

In a third way,

6537 = 6 × thousands + 5 × hundreds + 3 × tens + 7 × ones

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