A Rational Number is a Real Number that can be denoted in the form of a simple fraction. If you are wondering how to represent Rational Numbers on Number Line then this article is for you. You will know everything about what is a number line and how do we express rational numbers on a number line step by step. Check out solved examples on the representation of the rational numbers on a number line and solve similar kinds of questions easily.
Number Line – Definition
A number Line is a pictorial representation of numbers on a straight line. We can use it as a reference for ordering and comparing numbers. To the right side of the origin, we denote positive values and on the left side of the origin, negative values are expressed.
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Rational Numbers – Definition
In Simple Maths, we can define Rational Number as any Number that can be denoted in the form of p/q where p, q are integers and q ≠ 0.
How do you Represent Rational Numbers on a Number Line?
Follow the simple steps listed below for the representation of rational numbers on the number line. They are as such
- Firstly, draw a line and locate a point 0 i.e. origin.
- If the given number is positive mark it on the right side of the origin. if it is negative mark it on the left side of the origin.
- For denoting fractions divide each unit into values equal to the denominator of the fraction.
Rational Number Representation Using Successive Magnification
We can represent the decimal expansion on the number line using the successive magnification process. We know every rational number can be denoted as decimal expansions. Here, 1/3 = 0.33333……..
Step 1: Locate 0.3 on the number line and lies between 0 and 1
Step 2: Now represent 0.33 on the number line. We know 0.33 lies between 0.30 and 0.40
By magnifying numbers between 2 other numbers on the number line, we can represent the decimal expansion of rational numbers easily.
Solved Examples on Representation of Numbers on Number Line
Example 1.
Represent Rational Numbers 3/5 on the Number Line?
Solution:
Given Rational Number is 3/5
We know it is a proper fraction and positive number thus it lies on the right side of the origin. i.e. between 0 and 1.
Split the number line between 0 and 1 into 5 equal parts the number of times the denominator. The third part is the representation of rational number 3/5.
Example 2.
Represent Rational number 9/6 on the number line?
Solution:
Given Rational Number is 9/6
We know it is an improper fraction and a positive number thus it lies on the right side of the origin. i.e. between 0 and 1.
Improper Fraction 9/6 expressed in the mixed fraction is 1 3/6
Example 3.
Represent Rational Number -2/4 on a Number Line?
Solution:
Given Rational Number is -2/4
We know it is a proper fraction but a negative number thus it lies on the left side of the origin. i.e. between 0 and -1.
Proper Fraction -2/4 expressed on the number line is as follows. We will split into 4 equal parts and then the 2nd part between 0 and -1 is -2/4.
