What Is The Difference Between Rational And Irrational Numbers

by Rohan Mathew
What Is The Difference Between Rational And Irrational Numbers

The numbers derived from the basic ten digits in arithmetic have been classified into so many different groups based on their purpose or properties. Before discussing the difference between rational numbers and irrational numbers, let us talk about the various numbers. We are familiar with real numbers, fractions, natural numbers, whole numbers, prime numbers, and so on. Numbers help us in communicating the amount or the measure with the help of counting hence making it absolutely important to have a clear understanding of the different sorts of numbers.

We know that any positive or negative whole numbers are referred to as the integers. These are also the counting or the natural numbers. The whole numbers are the natural numbers, including the zero. Then comes the fraction, which is a part of the whole. It is expressed as two integers, numerator, and the denominator separated by a fraction bar.  

Real numbers are both rational and irrational numbers. Real numbers can be defined as any number that can be located on a number line. A rational number is defined as that number which can be written as a fraction, with integers in the numerator and denominator. The denominator can be any natural number but not zero. We can also say that all the whole numbers are rational numbers since they can be written as divided by one. Example, 5/1. Also, negative rational numbers also exist like -4/5. The word rational comes from the word ratio. 

Irrational numbers are the opposite of rational numbers, meaning that they cannot be expressed in terms of fractions or, infact, as the ratio of two integers. Example “pi” is an irrational number. Pi is referred to as the ratio of the circumference of the circle to its diameter. This number pi can be easily expressed as a fraction which is 22/7, but when we try to convert it to a decimal, the digits after the decimal point are never-ending, as we can see here 22/7= 3.1415926535897932…… 

Let us see some more examples of the irrational numbers, which are as:

The square root of 2, infact, the square root of all prime numbers, is irrational. Euler’s number e, where e = 2.718281828459045235360287471352. Then the golden ratio which is a mathematical formula. It is an irrational number that can be used in a variety of areas, including computer science, design, sculpture, and architecture.

One thing to remember about pi is that pi multiplied by pi produces an irrational number, but the square root of two produces a rational number when multiplied by itself. As a consequence, multiplying random numbers yields both rational and irrational results.

Math worksheets are a fantastic way to reinforce the idea of numbers, and they provide students with a lot of practice problems. Many websites now have worksheets that can be downloaded. One can visit Cuemath as it is an established education brand online. They have several kinds of visually appealing as well as interactive worksheets which help ease the anxiety of kids while allowing them to practice and learn smoothly.

Some more facts regarding rational and irrational numbers are:

-If an irrational and a rational number are added together, the result is still an irrational number.

-Any irrational number multiplied by any nonzero rational number yields an irrational number.

-It is not necessary that the product of multiplying a rational number is necessarily irrational.

-The sum of two irrational numbers is irrational at times and rational at others.

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