Rational numbers on a number line

A rational number is any real number that can be expressed as a simple fraction or ratio. By definition, it is any number which can be written in the form of p/q where p and q are any two integers and q not equal to zero (q ≠ 0).Rational numbers thus can be positive or negative.If we take a closer look on counting numbers, all of them are rational numbers with denominator 1. A set of rational number is denoted by the letter Q.

Rational numbers

Real numbers

Rational numbers on a number line

You have learnt how to represent whole numbers and integers on the number line. Similarly, we can also represent a rational number on a number line.

As we know, every positive number occupies space right to the origin while the negative numbers are present on the left side of the origin. Let us learn to represent a rational number on a number line with few steps.

  • Draw a line and locate the point having the coordinate as ‘0’. This point is known as the origin.

 Rational numbers

  •  If the given number is positive, locate it on the right side of the origin. If it is a negative number, locate it on the left side of zero.
  • Divide each unit into the values which are equal to the denominator of the fraction. For example: for representing 4/5 on the number line you need to divide each unit into 5 subunits.

Example: Represent 2/3 on a number line.

Solution: 2/3 is a positive rational number and it is known that 2/3 is less than 1 and greater than 0. Therefore, 2/3 lies between 0 and 1 on the number line.

Here, the denominator is 3 so we will divide each unit length into 3 subunits between 0 and 1.

Rational numbers

We know every rational number can be expressed as decimal expansions. Here,

⅔= 0.6666666666666667

We can represent this decimal expansion on the number line through the process of successive magnification.

Step 1: Represent 0.6 on the number line. 0.6 lies between 0 and 1 on the number line.

Rational numbers

Step 2:Represent 0.66 on the number line. 0.66 lies between 0.60 and 0.70 on the number line.

Rational numbers

Step 3: Represent 0.666 on the number line. 0.666 lies between 0.66 and 0.67.

Rational numbers

By magnifying the numbers between two other numbers on the number line, we can represent a terminating decimal expansion of rational numbers easily.

To practice more problems on the representation of rational numbers on a number line, download Byju’s-The Learning App.

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