Rational Numbers on a Number Line

The numbers that can be represented in the form of ratios are known as rational numbers. Rational numbers can be written in p/q, where q is not equal, not zero, and p, q are integers. In addition, rational numbers can be positive or negative.

Like other numbers, rational numbers can also be represented on a number line. A number line is a line with 0 as its origin. The right side of the number line denotes positive numbers, and the left side of the line denotes negative numbers.

Rational numbers can be of two types – proper fractions and improper fractions.

Proper fractions – Those fractions whose numerator is less than the denominator are called proper fractions. These fractions are less than one but greater than 0.

Improper fractions – Those fractions whose numerator is greater than the denominator are called improper fractions. They are easy to plot after they are converted to mixed fractions.

Rules to Represent Numbers on a Number Line

1. Mark the positive side of the number line, i.e. the right side, to represent the numbers correctly.
2. Mark the origin 0 as the centre of the number line.
3. Make appropriate scales on the number line with equal parts between two integers on both sides of the number line.
4. We cannot change scaling or keep different scales in opposite directions. On both sides, scaling should be similar.
5. After putting the value, mark the scale on the number line to denote the point correctly.

Example

Denote 2/3 on the number line.

Solution

We know the value of 2/3 is greater than 0. Hence, it will be placed on the right-hand side of the number line. Put accurate scaling, i.e. divide parts between numbers equally, as shown in the picture to mark 2/3 on the number line.

Representing Rational Numbers on a Number Line Using Successive Magnification We can denote numbers on a number line using successive magnification. Let us take the above example and represent 2/3 on the number line.

We know the value of 2/3 is 0.666666. So let us take 0.6 for our convenience.

1. As shown in the figure, we need to make equal partitions between 0 and 1 to represent 0.6.
2. Then we need to divide scales between 0.6 and 0.7 to mark another 0.67 on the number line.
3. Then we need to divide another ten equal parts between 0.66 and 0.67 to mark another 0.667 on the number line.
4. By continuing this method, we can represent accurate values on the number line.

Fun facts about the number line

1. Basic knowledge of fractions is mandatory to understand number lines. Without fractions, one cannot figure out where the number will go on the number line. Therefore, one must know what improper and proper fractions are.
2. Once a person knows fractions, it is easy to locate numbers by making appropriate conversions according to their ease. This saves time and enhances the understanding of number lines for various arithmetical operations as well.