As a student, what do you do at school before every period starts? You take out the books required for that period and arrange your things like notebook, pen and pencil in an order. Isn’t it? At home, your parents tell you to keep your shoes in a designated place, your books in the study and so on. Have you ever thought about why it is important to keep things in an orderly fashion?

Well, the answer is because when things occupy a specific place, they are easy to interpret, use and fetch. It makes everything more meaningful and time-efficient. The same applies to Numbers as well. Have you ever seen any number for example, 589 written as 5   8        9 or in any other haphazard manner? That’s because there is a standard to write the number in a way for everyone to understand. Let us learn the Place Value and Expanded Form of Numbers in this article.

What is the ‘Place Value’ of a Number?

The concept of place value of a number forms the basis of the number system. The place value of a number determines the value of the number depending on its position in the digit.

Let us try to understand it with a simple example. The number 45,671. Observe the position of each digit in this number. Now, let’s change the position of one or two digits and see what happens. Let’s assume that the resulting number is 71,456. Note that the digits 71 which were in the 4th and 5th position in the first number now occupy 1st and 2nd position. As a result, the value of those digits has also changed.

How to Find the Place Value of a Number?

Let us take another example of a number in order to understand the place value of each digit – 6,185. In expanded form, this number could be written as six thousand one hundred and eighty five. We will come to the expanded form of numbers in a while.

In this example, we start from the right extreme position, which is 5 and call this position as unit place. The number 8 is in ten’s place, number 1 is in hundreds place and number 6 is in thousand place. Therefore, starting from the unit place, we can continue to tens, hundreds, thousand, ten thousand, lakh, and so on.

As already mentioned at the beginning, the place value of a number depends on its position. Applying this method, we say the place value of 5 is ‘5 ones’ which is five, place value of 8 is ‘8 tens’ which is ‘eighty’’. Similarly, the place value of 1 is ‘1 hundred’ which is nothing but hundred and finally, the place value of 6 is ‘6 thousands’ which is ‘six thousand’.

What is the Expanded Form of Number?

In the previous paragraph which mentions ‘Six thousand’ and ‘Eighty’, this is called the expanded form of the number. When you add the sum of each digit multiplied by its pace value, the result will be the expanded form of the number.

How to Write the Expanded Form of Number?

Let us understand the process of writing the expanded form of number with an example.

Example 1: Find the expanded form of 8,534

To solve this, let us start by finding the place value of each number.

Place value of 4 is 4

Place value of 3 is 30 * 10 = 30

Place value of 5 is 5 * 100 = 500

Place value of 8 is 8 * 1000 = 8,000

Now let us add.

4+30+500+8000

The answer is 8,534. It can be written as Eight Thousand Five Hundred and Thirty Four.

Example 2: Find the expanded form of 67,910.

Applying the place value to each digit, this time from left to right (Note that the value of the number does not vary when you go from right to left or from left to right).

Place value of 6 is 6 * 10,000= 60,000

Place value of 7 is 1000 * 7 = 7,000

Place value of 9 is 100 *9 = 900

Place value of of 1 is 10 * 1 = 10

Place value of 0 is 1 * 0 = 0

Now let’s add.

60,000+7000+900+10+0

The answer is 67,910. It can be written as Sixty Seven Thousand Nine Hundred and Ten.

We hope this article on Place Value and Expanded Form of Numbers helps you. If you have any academic queries, do reach out to us. You can write us a mail at [email protected] or call 1800313002020 (Toll) & +91-7666597555. We will be happy to help you.

For more such articles follow Embibe.