Rational Numbers on Number Line

Rational numbers are defined as any number that can be represented as the ratio of two integers where the denominator is not equal to zero. Rational numbers on a number line are the way of representing positive and negative rational numbers visually.

Rational numbers are defined as a number that can be represented in the form of p/q where p and q are integers and q ≠ 0. Representation of rational numbers on a number line is defined as plotting or graphing positive and negative rational numbers on a number line. Number line helps us to find an infinite number of rational numbers between any two rational numbers by increasing the number of divisions.

The rational number are the numbers which can be represented on the number line. In the figure below, we can see the number line. There are positive numbers, zero and negative numbers on the number line. Suppose you want to plot the number  23 on the number line.

Now, first draw the number line and divide the line. To represent rationals, we divide the distance between two consecutive part into ‘n’ number of parts. Here in this example, we will divide the distance between 0 and 1, 1 and 2 and so on in three equal parts. How do you know that we are supposed to divide it into three divisions? The denominator tells us. The number of divisions will be equal to the denominator.

Construction

1.  Draw a line and first mark zero on the number line.
2. Now from 0, divide the line into three equal parts on the R.H.S of 0. The third point will be marked as 1.
3. Repeat the same steps to locate the number 2 on the number line.
4. Now take the same length on L.H.S of the zero and divide the line into three equal parts so that we can locate -1 on the number line.
5. The most important thing before locating  2/3 on the number line is to write the divisions.
6. Now the point after 0 will be denoted by 1/3,
7. Now increase the numerator by 1 and so the next point that means the third point will be 2/3.
8. Exactly, in the same way, denote the points on the L.HS of o.
9. Now locate 2/3 and name it as point P.

Example

Now let us see another example. Represent -3/4 on the number line.

Construction

1.   Again draw a line and mark zero on the number line.
2. Now as the denominator is 4, divide the line into four equal parts on the L.H.S of 0. The fourth point will be  -1.
3. Now repeat the same steps to locate the number -2.
4. To write the divisions the point after 0 will be denoted by -1/4.
5. Now increase the numerator by 1 and so the next point that means the third point will be -2/3.
6. Now locate -1/4 on the number line and name it as point P.
7. Exactly, in the same way, denote the points on the R.H.S of o.

In the same way, we can locate any number, may it be the positive number or negative number. In a rational number, the denominator tells the number of equal parts into which the first unit is to be divided.