Rational and Irrational – A Crucial Property of Numbers

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Numbers are something without which it is hard to imagine our life. Just like alphabets numbers are the foundation of mathematics. People may think that numbers are simply combinations of numbers from one to nine but it is not that simple. Numbers possess a lot of different properties. We can differentiate them based on any particular property that they show. For example, if a number is divisible by two, then it falls into the category of even numbers. Similarly, there is a lot of classification of numbers. In this article, we will be discussing two such classifications of numbers. Rational numbers and irrational numbers are the topics we are about to discuss. They hold a lot of importance in various subjects. Hence, students must understand these topics properly.

Rational numbers

Rational numbers are numbers that not only students but everyone observe around them. When one observes the rational word closely, one may conclude that it is something related to ratio. If there is a number that can be represented in the form of p/q where both p and q can be integers and also q is not equal to zero, then the number is known as a rational number. There is a high probability that a person may get confused between rational numbers and fractions, but they should know the basic difference between the two numbers. Rational numbers, as we discussed above are made up of integers, whereas fractions are the numbers that are made by whole numbers.

If someone thinks that a rational number is only of one type then they are wrong. A rational number has many types. Decimal numbers can also consider as rational numbers if they fulfil a necessary condition. Decimal that is terminating is also rational numbers. Terminating decimals are those numbers that have an end. One important point to keep note of is that all the integers also fall into the category of the rational number. As all integers are rational numbers it directly proves to us that all whole numbers are also rational numbers. A student should know rational numbers to easily handle problems related to numbers.

Irrational numbers

These are the numbers that are impossible to depict in the form of ratios. One can also say that those numbers that are not rational are known as irrational numbers. These numbers can never be represented in the form of a fraction. One way of determining whether a number is irrational or not is by observing the decimal number. When we perform certain operations on two irrational numbers then the result can be rational or irrational. For example, the sum of irrational numbers can give us rational or irrational number as an answer.

There are many examples of irrational numbers that we deal with in our everyday life. One of the most famous irrational numbers is pi apart from it, square roots of 2, 3,5 and many more such numbers are also irrational. No one can determine the finite values of irrational numbers. For example, the value of pi is never-ending. Students need to deal with irrational numbers on regular basis. Hence, they should know to be able to differentiate between the numbers whether it rational or irrational.

In the above article, we have tried to focus and discuss both the topics of rational and irrational numbers in full depth. Numbers are the basic quantity that needs to be clearly understood by the students. As, if their basics are clear then they will not face difficulties in solving higher problems of mathematics. These minor things that many students ignore are of great importance. Students should understand the concept behind them and practice them as much as possible. If students face any difficulty in understanding such topics which are directly related to mathematics. They should take the assistance of the online platform Cuemath. Cuemath helps students to clear their concepts and easily solve problems related to them. Cuemath math experts are providing the best education to children. They are known all over the world for their way of teaching.

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