A number line with decimals represented on it is called a decimal number line. It helps to compare decimals and calculate more precisely where there are minor differences in values.
Decimal Number Line
In the above figure, we divided the line segment joining 0 and 1 into 10 equal parts, each of the parts representing a decimal number.
Each decimal can also be written in a fraction form; for example 0.1 = ${\dfrac{1}{10}}$ , 0.2 = ${\dfrac{2}{10}}$, 0.3 = ${\dfrac{3}{10}}$, and so on.
Thus, plotting decimal numbers on a number line differs from plotting fractions only in their representation.
Fractions and Decimals on a Number Line
As a decimal number always lies between two integers, it can be represented by separating its integer and the fractional part.
Like other real numbers, decimal numbers also increase from left to right on a number line. In the above figure, we can see 0 < 0.1 < 0.2 <0.3 <…..<1
So if we want to compare 0.2 and 0.7, as 0.7 lies to the right of 0.2, 0.2 < 0.7
How to Plot Decimal Numbers on a Number Line
To plot a decimal number on a number line, we first draw the number line with 0 as the reference point. The numbers rights of 0 are positive decimal numbers, and to the left of 0 are negative decimal numbers.
Number Line with Decimals
The above figures shows each region from 0 to 1 and from 0 to (-1) are divided into 10 equal parts, with positive and negative decimal numbers between them.
Now, we can plot any decimal number (positive or negative) on the number line.
Positive Decimal Numbers on Number Line
To represent a positive decimal number involving tenths, we first identify the two integers found at the two ends of the decimal. Then, the region between those two numbers is divided into 10 equal parts.
For example, to plot 0.8, we follow the steps below
Step 1: The integers 0 and 1 are marked, and the region from 0 to 1 is divided into 10 equal parts, with each part increased by 0.1 to the right starting from 0.
Step 2: We move the number of steps to the right starting from 0 based on the rightmost value of the digit after the decimal point. So here we move 8 steps to the right starting from 0.
Thus 0.8 is plotted on the number line.
Find the decimal number 1.4 on a number line.
Solution:
As 1.4 lies between the integers 1 and 2, we mark the integers on the number line and divide the region from 1 to 2 into 10 equal parts. Next, moving 4 steps to the right starting from 1 (as the rightmost digit after the decimal point is 4), we find 1.4 on the number line.
Now let us now plot the decimal number 3.45 on the number line. The given decimal number 3.45 includes a digit in the hundredth place. It lies between 3 and 4, more specifically between 3.4 and 3.5.
Step 1: We first divide the region between 3 and 4 into 10 equal parts, each increasing by 0.1 to the right starting from 3.
Step 2: We plot numbers from 3.4 to 3.5 as 3.45 lies between them and make 10 more divisions.
Step 3: As 5 is the digit at the extreme right of 3.45, we move 5 steps to the right of 3.4 and find 3.45 on the number line.
Represent the decimal number 8.24 on a number line.
Solution:
The given decimal number 8.24 lies between the integers 8 and 9 and, more specifically, between the decimal numbers 8.2 and 8.3. So the region from 8.2 to 8.3 is divided into 10 equal parts, and moving 4 steps to the right starting from 8.2, we find the decimal number 8.24 on the number line.
Similarly, to find a decimal number in thousands, the region of integers between where it lies is divided into 1000 equal parts, each part representing ${\dfrac{1}{1000}}$ or 0.001.
Locate the decimal number 1.009 on a number line.
Solution:
The decimal number 1.009 exists between the integers 1 and 2. More specifically, it exists between the numbers 1 and 1.10. In particular, it lies between 1.00 and 1.01. So we divide the segment joining 1.00 and 1.01 into 10 equal parts, where the number of divisions between 1 and 2 is 103. Moving 9 steps to the right starting from 1 gives the number 1.009 on the number line.
So to place a decimal number on a number line, we find the number of total digits after the decimal point, say n and divide the region between the two integers where the decimal lies in 10n equal parts.
Negative Decimal Numbers on Number Line
Plotting negative decimal numbers on a number line is similar to plotting positive ones, except that the operation is performed to the left of 0.
For example, to plot (-1.6) on a number line, we follow the steps below
Step 1: We first mark the numbers (-1) and (-2).
Step 2: The segment joining (-1) and (-2) is divided into 10 equal parts, each of them decreasing by 0.1 from right to left starting from (-1).
Step 3: Starting from (-1) and moving 6 steps to the left, we find (-1.6) on the number line.
Find the decimal number (-5.49) on a number line.
Solution:
As the decimal number (-5.49) lies between the integers (-5) and (-6) and, more specifically, between the decimal numbers (-5.4) and (-5.5), the area from (-5.4) to (-5.5) is divided into 10 equal parts. Here we move 9 steps to the left starting from (-5.4) and find the number (-5.49) on the number line.
