Representation of Decimals on Number Line: The whole number and fraction are expressed using the decimal number system. A decimal point is a dot placed between two integers in a group of numbers called a decimal. Integers or whole numbers are numbers to the left of the decimal point, whereas decimal numbers are numbers to the right of the decimal point.

When we represent decimals on a number line, we can see the intervals between two integers, which helps us understand the fundamental concept of decimal number formation. On a number line, we divide the unit length between 0

equal parts to represent a decimal number. There are 1.1,1.2,1.3,1.4,1.5,1.6,1.7,1.8,and 1.9 between any two integers, such as 1and 2.

$1$

and 2.n order to understand the concept of decimals, let us make a square table with 1 row and 10 columns, as shown in the figure.

Let us fill four of these blocks, as shown below

The fraction of colored blocks to the total blocks can be written as 4/10. Another representation for the same can be given in terms of decimals, like 0.4. Here 0.4 = 4 * or can be written as 4 tenths.

Similarly, if we take a square of 10 rows and 10 columns, we get 100 small squares. If we colour 27 of these blocks, the fractional representation can be written as 27/100.

Here 27/100 = 27*1/100 = 27 hundredth which is represented in the decimal form as 0.27.

So when we have a number 2.34, it is equivalent to 2 + 3 tenths and 4 hundredths.

How to Represent the Decimals on the Number Line?

We know how to represent whole numbers on the number line. Let us consider the image shown below. Here, the digits 0 and 1 are represented on the number line.

If we divide the number line into two equal parts, as shown in the figure below, what value does mid-point hold? We will say half of what the graduation between 0 and 1 holds.

So, the point represents (1-0)/2 = 0.5

In order to represent decimals on the number line, we divide the section between two whole numbers as per the places after decimal present in the number to be represented.

Decimal Representation on Number Line Examples

Example 1:

Represent 0.8 on the number line.

Solution:

As we know, the number 0.8 is equivalent to 8 tenths, so we divide the section between 0 and 1 into 10 equal parts. Now, stepping 8 points from 0 towards 1 gives us 0.8.

Example 2:

Represent 8.6 on the number line.

Solution:

The number 8.6 = 8 + 0.6

We start from the number 8 on the number line and divide the section between 8 and 9 into 10 equal parts. Now, taking 6 steps from 8 towards 9 gives us the representation of 8.6