Difference Between Rational And Irrational Numbers In Tabular Form

Rational and irrational numbers are two very essential types of numbers in mathematics. In most of the mathematics papers, a number is given and the students are asked to get an idea whether it is a rational number or an irrational number. The students can easily get an idea about the rational and irrational numbers by getting an idea about the difference between rational and irrational numbers. Here, we will try to explain rational and irrational numbers with the help of examples.

Table of rational and irrational numbers

If you don’t have enough idea about the table of rational and irrational numbers, it is almost impossible for you to differentiate the rational numbers from the irrational numbers. The main points of this table are given below;

    1)    All the perfect squares are rational numbers i.e 16 is a rational number. Its reason is that 16 is a perfect square of 4.

    2)    All the surds are irrational numbers. √3 is an irrational number. Its reason is that √3 is not a perfect square of any real number.

    3)    All the terminating decimals are rational numbers. Terminating decimals are those decimals which stop the division process after the point. For example, 2.55 is a terminating decimal.

    4)    All the non-terminating and non-repeating decimals are irrational numbers. Non-terminating and non-repeating decimals are those decimals which repeat the same numbers after the point. For example, 2.523567839402…. is a non-terminating and non-repeating decimal.

    5)    All the repeating decimals are rational numbers. The numbers that repeat the same words are repeating decimals. For example, 2.55555…. is an essential example of repeating decimals. 

Is √2 is a rational or irrational number?

After understanding the difference between rational and irrational numbers, we are in a position to get a clear idea of which number is rational and which is irrational. If we take an overview of √2, we can get an idea that √2 is a surd. From the table of difference between the rational and irrational numbers, we can get an idea that all the surds are irrational numbers. As √2 is a surd, therefore, we can say that √2 is an irrational number.

Is √4 is a rational or irrational number?

√4 is a perfect square. After solving it, we can get its answer as 2. From the table of rational and irrational numbers, we also get an idea that all the perfect squares are rational numbers. As √4 is a perfect square of 2, therefore, we can say that √4 is a rational number.

Is 9/7 is a rational number or an irrational number?

Before getting an idea either 9/7 is a rational number or an irrational number, we have to divide it. After dividing 9/7, we get the answer 1.285714….. It means that it is non-terminating and non-repeating decimal. From the table of rational and irrational numbers, we also know that all the non-terminating non-repeating decimals are irrational numbers. Therefore, we can also say that 9/7 is also an irrational number.

Is 3/2 is a rational number or an irrational number?

Like 9/7, if we want to get an idea about 3/2, it is also necessary for us to divide it. After dividing 3/2, we get the answer 1.5.1.5 is a terminating decimal. From the table of rational and irrational numbers, we know that all the terminating decimals are also rational numbers. Therefore, we can say that 3/2 is a rational number.

Is 2/3 is a rational number or an irrational number?

After dividing 2/3, we get the answer 0.666666…… It means that it is non-terminating and repeating decimal. From the table of rational and irrational numbers, it is clear that all the non-terminating and repeating decimals are irrational numbers. Therefore, we can say that 2/3 is a rational number.

Conclusion

To sum up, we can say that there are two things to differentiate the rational numbers from the irrational numbers. First of all, we should take an overview of the table of rational and irrational numbers. This table will provide us with a clear idea about rational and irrational numbers. Secondly, we should get an idea about the nature of the given numbers. After comparing these numbers with this table, we will be in a better position to differentiate between these two numbers.