Difference between RATIONAL and IRRATIONAL numbers
In this new lesson from a Teacher we are pleased to bring you a very important topic within the world of mathematics: in this lesson we will see the difference between rational and irrational numbers. For this reason, we will begin by presenting a brief description of each of these numbers, and then highlighting their most important differences. As is customary for us, we will be supporting the theoretical explanation with some practical examples, as with him video of the professor Claudia López that will serve as a complement in this lesson.
Index
- Main differences between rational and irrational numbers
- What are rational numbers
- What are irrational numbers
- Examples of rational numbers
- Examples of irrational numbers
Main differences between rational and irrational numbers.
The difference between rational numbers and irrational numbers it is quite obvious.
- First, and perhaps most important, is the fact that, while rational numbers can be expressed in the form of fraction, the irrational numbers no they can be expressed this way.
- Rational numbers are quantities that can have a period in the decimal, or finite decimal and limited.
- In the case of irrational numbers, their decimals tend to infinity, that is, we cannot represent them in a fraction.
These would be the two biggest differences between rational and irrational numbers. In this aspect they are completely contrary (as can be seen in the following sections).
What are rational numbers.
The rational numbers are fractions that can be formed from integer numbers Y real. This means that rational numbers are real numbers that can also be expressed as a fraction, since we can calculate or know both the numerator and the denominator.
The name of rationals is the translation from English, rationals, witch reffers to to ratio, that is fraction. So, knowing that rational numbers are associated with a ratio, it will be easier to remember them.
Rational = Rational = Ratio = Fraction => Yes we can express them as a fraction of two whole numbers.
As we can see in the following diagram, the real numbers are divided between irrational numbers and rational numbers, which can be reduced to whole numbers and these to natural numbers.
In short, for theoretical purposes, we can say that a number is rational if we can express it as a fraction.
What are irrational numbers.
On the other hand, we have irrational numbers. This kind of numbers they are real numbers that cannot be expressed exactly, nor periodically. This means that irrational numbers cannot be expressed as a fraction because we do not know, or cannot calculate, the numerator or denominator.
The name of rationals is the translation from English, rationals, which refers to ratio, that is to say fraction. So, knowing that rational numbers are associated with a ratio, it will be easier to remember them.
Irrational = Irrational = Irratio = No Ratio = No Fraction => We cannot express them as a fraction of two whole numbers.
Later, in the following sections, we will give some examples of irrational numbers so that this theoretical aspect is more easily appreciated.
Examples of rational numbers.
We have already seen the theory and concept of these two numbers, now we are going to continue with some examples so that you can see the difference between rational and irrational numbers more clearly.
In the case of rational numbers, there is not too much mystery. Any number that can be expressed as a fraction is a rational number. For example:
48 is a rational number, because it can be expressed as a fraction.
Another slightly more complex example can be 3,5. This number is also rational, since it can be expressed as 7/2 which is a fraction, therefore it is rational. We know its numerator and denominator, since it has a finite decimal.
Examples of irrational numbers.
Now, in the case of irrational numbers, the difference is very clear, but you have to be attentive anyway.
An irrational number par excellence would be the number 𝝿 (Pi). We know that this number equals 3.1415926… up to infinity. That is, it does not have a decimal that we know, since it is not finite; therefore, we cannot express it as a fraction.
Another good example of an irrational number would be the roots. For example √3, is an irrational number because its decimals tend to infinity and we cannot express it in a defined fraction. However, not all roots are irrational numbers; the roots that can be calculated and their result is an exact number, are considered rational numbers.
There is the case of √4, we know that √4 = 2; so it can be expressed as a fraction, which means that it is a rational number.
The objective of this last example is to highlight the fact that not necessarily if a number is a root, it is automatically an irrational number, each case is different. As we have said before, what defines a rational or irrational number is whether or not it can be expressed as a fraction.
We hope this lesson has been helpful for this topic and as always, you know that you can count on all the material from a teacher who is available on our page, for this or any other subject with which you need support extra. We continue to encourage you in your studies and forward.
If you want to read more articles similar to Difference between rational and irrational numbers, we recommend that you enter our category of Arithmetic.
