## What are Rational Numbers?

A rational number is a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero, whereas an irrational number cannot be expressed in the form of fractions.

### Arranging Rational Numbers on a Number line

Real numbers are broadly classified into two types namely rational and irrational numbers. All these numbers can be represented on a number line. A number line is a straight line on which all the positive and negative real numbers are arranged towards the right and left of a fixed point called the reference point. The reference point on the number line is zero.

### Rational Numbers Vs Irrational Numbers

Rational numbers are those numbers that can be expressed in p/q form that is represented in a fraction from where q is never equal to zero. On the other hand, irrational numbers can not be represented in a ratio format or p/q form. Rational numbers include finite and recurring decimals whereas irrational numbers include non-recurring and non-terminating decimals. Both the numerator and denominator of a rational number is a whole number or positive integer whereas an irrational number can never be expressed in that format.

### Number Lines

Number Lines are nothing but a horizontal representation of numbers and their values on a line with equal intervals having certain values. Numbers with a particular sequence can only be expressed on a number line and this can be extended indefinitely on either side. Generally, zero is taken as a reference value and all the positive numbers or values are pointed to the right of the number line whereas all the negative values are marked to its left. It is comparatively easy to explain arithmetic operations like addition, subtraction, etc, on a number line.

### How to Show Rational Numbers on a Number Line

A rational number is a number that can be represented in the form of a fraction in which the value of the denominator is not equal to zero. If the denominator is zero, then the number is not a rational number. Rational numbers include whole numbers, positive and negative integers, decimal numbers, and fractions. A detailed description of steps to be followed for plotting the rational numbers on a number line for different types of numbers is elaborated in the subsequent sections.

### Plotting Rational Numbers on a Number Line (Integers)

Step 1:

Construct a number line with zero as a reference point, positive integers on the right of zero and negative integers on the left of zero.

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Step 2:

The given number is represented at a point indicating that number towards the right if the number is positive and towards the left if the number is negative.

The blue spots in the above figure indicate -3, 2 and 4 as the representation of rational numbers on a number line.

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### Plotting Rational Numbers on a Number Line (Number with a Decimal point)

Step 1:

If the number has a decimal point, it should be first converted into the form of a fraction.

Step 2:

If the fraction is improper, the steps for plotting improper fractions on the number line should be followed. If not, the steps to represent proper fractions should be followed.

### Plotting Rational Numbers on a Number Line (Improper or Mixed fraction)

Step 1:

If the given fraction is an improper fraction, it should be converted into a mixed fraction. The mixed fraction consists of a whole part and a proper fraction part. The whole part is generally a positive or negative integer.

Step 2:

Construct a number line with zero as a reference point, positive integers on the right of zero and negative integers on the left of zero.

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Step 3:

Identify the point indicating the whole number part of the fraction on the number line. The distance between this point and the point indicating the immediately next whole number part is divided into a number of parts equal to the denominator in the fraction part of the mixed fraction.

Step 4:

The part indicating the digit in the numerator of the fraction part in the mixed fraction indicates the given rational number.

### Plotting Rational Numbers on a Number Line (Proper fraction)

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Step 1:

Construct a number line with zero as a reference point, positive integers on the right of zero and negative integers on the left of zero.

Step 2:

Divide the distance between the points indicating 0 and 1 (-1 for negative rational numbers) into a number of parts equal to that of the denominator of the fraction.

Example: To represent -3/5 on a number line, the distance between 0 and 1 should be divided into 5 equal parts.

Step 3:

The part indicating the value in the numerator is the point indicating the given rational number.

Example: The figure below shows the representation of -3/5 on a number line.

### Fun Facts about Arranging Rational Numbers on a Number Line

To understand the representation of rational numbers on a number line, the basic concept of types of fractions is mandatory. Proper fractions are the fractions with the value of numerator less than the value of denominator and the improper fractions are the fractions with the value of denominator less than that of the numerator.

While arranging rational numbers on a number line, the rational numbers that are proper fractions lie between 0 and 1, and the rational numbers that are improper fractions are first converted to a mixed fraction and then represented on a number line.

### Conclusion

Rational Numbers are the foundation of mathematical equations. If it weren’t for these, we wouldn’t have linear or binary equations. They substantiate numbers. This article focuses on Rational numbers, their applications, and how to plot them. Go through it properly for a better understanding.

## FAQs on Rational Numbers on a Number line

**1. What are Rational Numbers?**

Rational numbers are the numbers that can be represented in the form of a fraction in which the numerator and denominators are integers and the denominator is not equal to zero. Also, the numerator and denominator should be coprime to each other. Mathematically, any number that can be represented as x/y where ‘x’ and ‘y’ are coprime and y ≠ 0.

**2. How to Represent Rational Numbers on a Number Line?**

The below steps are followed while plotting Rational Numbers on a Number Line:

The first step to be considered to show rational numbers on a number line is to check whether it is a proper, improper, or mixed fraction representation.

If the given rational number is a proper fraction, then the distance between zero and one on the number line is divided into a number of parts equal to the denominator and the part indicating the value of the numerator is the point that gives the representation of rational numbers on a number line.

If the given rational number is an improper fraction, it should be first converted into a mixed fraction. The rational number lies between the whole number represented in the mixed fraction and the immediate consecutive number. The distance between the whole number and the immediate consecutive number is divided into a number of equal parts as indicated by the denominator. The part indicating the number in the numerator is the point indicating the given number.

If the number is a decimal, it is first converted into a fraction, and then the steps for plotting rational numbers on a number line when it is a fraction are followed.

**3. What are decimals and how are they plotted on a number line?**

Decimal numbers are one among the different types of numbers, others are real numbers, rational numbers, composite numbers etc, decimals are used to represent an integer and a non-integer in a standard form. They are further divided into recurring decimals, non-recurring decimals and fractions. To represent these decimals on a number line, follow the below steps:

The decimals are to be converted to a fraction to be plotted on a number line.

If the fraction is proper, construct a number line with zero as a reference point and plot the positive numbers to the right of zero and negative numbers to the left of zero.

Divide the distance from zero to either end equally and number them.

The part of the numerator of a fraction is to be marked as an individual value on the number line to get a given point.