How to Plot Rational Numbers on a Number Line: Simple Steps
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.
(Image will be uploaded soon)
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.
(Image will be uploaded soon)
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.
(Image will be uploaded soon)
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)
(Image will be uploaded soon)
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 Explained
1. What is the basic definition of a rational number as per the NCERT syllabus?
A rational number is any number that can be expressed in the form of a fraction p/q, where 'p' (numerator) and 'q' (denominator) are integers, and the denominator 'q' is not equal to zero. For example, 3/4, -2/5, 7 (which is 7/1), and 0 (which is 0/1) are all rational numbers.
2. What are the general steps to represent a rational number on a number line?
To represent a rational number on a number line, you can follow these general steps:
Draw a straight line and mark a point as zero (0). Mark positive integers (1, 2, 3,...) to the right of zero and negative integers (-1, -2, -3,...) to the left at equal intervals.
Identify the two consecutive integers between which the rational number lies. For a proper fraction like 4/5, it lies between 0 and 1.
Divide the segment between these two integers into a number of equal parts that matches the denominator of the fraction.
Starting from the smaller integer, count forward by the number of parts equal to the numerator to find the exact point.
3. How would you represent the rational number 3/4 on a number line as an example?
To represent 3/4 on a number line, first, you identify that it is a positive number and lies between 0 and 1. You then divide the segment between 0 and 1 into four equal parts, because the denominator is 4. Finally, you count three parts to the right from 0. The third mark represents the position of 3/4 on the number line.
4. How is a negative rational number, like -2/3, represented on a number line?
Representing a negative rational number follows the same logic but on the left side of zero. For -2/3, you would look at the segment between 0 and -1. You divide this segment into three equal parts (as the denominator is 3) and then count two parts to the left from 0. This point marks the location of -2/3.
5. What is the method for plotting an improper fraction, such as 7/5, on a number line?
For an improper fraction like 7/5, it's best to first convert it into a mixed fraction. Here, 7/5 is equal to 1 2/5. This shows that the number lies between the integers 1 and 2. You then divide the segment between 1 and 2 into five equal parts (the denominator). The second part after 1 will be the point representing 7/5.
6. Why is a number line a useful tool for comparing two different rational numbers?
A number line provides a clear visual representation of the order of numbers. When you plot two rational numbers, the number that is farther to the right is always greater. For example, by plotting both 1/2 and 1/4, you can instantly see that 1/2 is to the right of 1/4, which means 1/2 > 1/4. This is more intuitive than finding a common denominator, especially with a mix of positive and negative numbers.
7. Are integers and zero also considered rational numbers, and how do they fit on the number line?
Yes, all integers (including positive, negative, and zero) are rational numbers. They can be expressed with a denominator of 1. For example, the integer 5 is the rational number 5/1, and -3 is -3/1. Zero is the rational number 0/1. On the number line, these rational numbers correspond directly to the integer markings we use as reference points.
8. How do terminating and recurring decimals relate to representing rational numbers on a number line?
Both terminating decimals (like 0.5) and non-terminating recurring decimals (like 0.666...) are rational numbers because they can be converted into the p/q fraction form. For instance, 0.5 is 1/2, and 0.666... is 2/3. Once converted to their fraction form, they can be plotted precisely on a number line using the standard method, proving that they have a specific, fixed location.
