Expanded Form in Mathematics - Practic Education

In Mathematics, we have learned numbers and their properties. Also, we have come across various forms of numbers in different types, such as integers, fractions, whole numbers, etc. The representation of numbers helps us to study and understand them.

A number can have one or more than one digit. Each digit has its position or place value such as ones, tens, hundreds, thousands, ten-thousands and so on. One of the forms that help us to determine the position of a digit in a number is the expanded form. From the word itself, we can identify to expand a number. For example, 300 can be written as 3 x 100, in expanded form.

Expanded Form of Different Numbers

The expanded form of natural numbers is easy to represent. We can use the place value chart as given below.

Number	Ten Thousand	Thousands	Hundreds	Tens	Ones
23				2	3
123			1	2	3
1234		1	2	3	4
12345	1	2	3	4	5

In the above table, we can clearly understand the numbers and place values of each digit in it.

In number 23, 2 is tens place, and 3 is at ones place
In number 123, 1 is at hundreds places, 2 is at tens place, and 3 is at ones place
In number 1234, 1 is at thousands place and rest digits follow the same sequence from hundreds to ones places
In number 12345, 1 is at the ten-thousands place, and the rest digits follow the same sequence from thousands place to ones place.

Now the question comes, how to write these numbers in expanded form. Let us start with the first number.

23: Based on the place values of 2 and 3, we can write;

23 = 2 x 10 + 3

Hence this is the expanded form of 23.

Thus, we can say,

Expanded Factor Form = Sum of (Digit × Place Value)

Similarly, we can write the expanded form of other numbers.

123 = 1 x 100 + 2 x 10 + 3
1234 = 1 x 1000 + 2 x 100 + 3 x 10 + 4
12345 = 1 x 10000 + 2 x 1000 + 3 x 100 + 4 x 10 + 5

In this way, we can represent any natural number in expanded form. But what about the decimal or fractions? Let us understand the expanded form of fractions.

Expanded Form of Fractions

The fractions are the numbers that are represented by numerator and denominator. The numerator is the upper part, and the denominator is the lower part of the fraction. For example, ⅖ is a fraction. We have learned different operations performed on fractions directly, such as adding fractions, subtracting fractions, etc. But, to represent the fractions in expanded form, we need to convert them first in decimal form. After the conversion, we can write the decimal into expanded form. Let us see some examples.