Plotting rational numbers on a number line

A rational number is a fraction and is plotted on a number line as follows.

Basic rules of representing rational no. on number line

• If the rational no.$fraction$ is proper then, it lies between 0 and 1.

• If the rational no.$fraction$ is improper then, we first convert it to mixed fraction and then the given rational no. lies between the whole number and next whole number.

We use following steps to represent a rational number or fraction for example, $\frac{5}{7}$ on the number line.

Step 1 − We draw a number line.

Step 2 − As the number $\frac{5}{7}$ is a positive number, it lies on the right side of zero.

Step 3 − So, after zero mark, we have $\frac{1}{7}, \: \frac{2}{7}, \: \frac{3}{7}, \: \frac{4}{7}, \: \frac{5}{7}, \: \frac{6}{7},$ and ($\frac{7}{7}$ = 1).

Step 4 − The rational number $\frac{5}{7}$ on the number line is shown as follows.

Plot $\frac{1}{4}$ and $1\frac{2}{4}$ on the number line below

Solution

Step 1:

$\frac{1}{4}$$A$ lies between 0 and 1; $1\frac{2}{4}$ $B$lies between 1 and 2

Step 2:

Each division is divided into four parts as the bottom of the fractions is 4.

$\frac{1}{4}$ is the first mark after 0, therefore point A represents $\frac{1}{4}$

$1\frac{2}{4}$ is the second mark after 1, so point B represents $1\frac{2}{4}$

Plot $\frac{5}{8}$ and $2\frac{3}{8}$ on the number line below

Solution

Step 1:

$\frac{5}{8}$ 8 $A$ lies between 0 and 1; $2\frac{3}{8}$ $B$lies between 2 and 3

Step 2:

Each division is divided into eight parts as the bottom of the fractions is 8.

$\frac{5}{8}$ is the fifth mark after 0, therefore point A represents $\frac{5}{8}$

$2\frac{3}{8}$ is the third mark after 2, so point B represents $2\frac{3}{8}$