Writing Numbers in Expanded Form

What is the expanded form of a number?

An expanded form is a way to write a number by adding the place values of its digits. The different place values are Ones, Tens, Hundreds, Thousands, Ten Thousands, Hundred Thousands, Million, Ten Million and so on.

You can refer to the place value chart to understand the place value in a number.

Let’s understand with an example: 6,273

6,273 is in standard form.

We can use many ways to show numbers in expanded form.

Method 1. To expand the number 6,273, we separate a number according to their place value then expand it to show the value of each digit.

The value of digit 6 at Thousands place = 6000,
The value of digit 2 at Hundreds place = 200,
The value of digit 7 at Tens place = 70,
The value of digit 3 at Ones place = 3,

Now, if you add the place value of each digit then you will get a total of 6,273.
6,000 + 200 + 70 + 3 = 6,273
So, the expanded form of 6,273 is 6,000 + 200 + 70 + 3

Another way to write numbers in the expanded form is to write the digits and convert all the coming numbers to zero.

Find the expanded form of 13,584

Thus, 10,000 + 3,000 + 500 + 80 + 4 is the expanded form of 13,584.

Method 2. In this method, we multiply the digit with its place value.

Example: 6,273
(6 x 1,000) + (2 x 100) + (7 x 10) + (3 x 1) = 6,273

Example: 13,584
(1 x 10,000) + (3 x 1,000) + (5 x 100) + (8 x 10) + (4 x 1) = 13,584

Method 3. Here, first the digit is written and then its place value is written (in words).

Example: 6,273
6 Thousands + 2 Hundreds + 7 Tens + 3 Ones = 6,273

Example: 13,584
1 Ten Thousand + 3 Thousands + 5 Hundreds + 8 Tens + 4 Ones = 13,584

Write the expanded form in different ways: 57369

(a) 50000 + 7000 + 300 + 60 + 9

(b) 5 × 10000 + 7 × 1000 + 3 × 100 + 6 × 10 + 9 × 1

(c) 5 ten thousands + 7 thousands + 3 hundreds + 6 tens + 9 ones

Try This!

Write the following numbers in their expanded form.

9,285 = _________________________________

3,876 = _________________________________

73,439 = _________________________________

Write the following numbers in their standard form.

5000 + 500 + 80 + 2 = __________________

20,000 + 1000 + 300 + 50 + 2 =____________________

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