Question

What is a real number, a whole number, an integer, a rational number, and an irrational number ?

Answer 1

Hint: In order to solve the question , we need to understand the given mathematical statement properly which contains the terms ‘a real number’ , ‘a whole number ‘ , ‘an integer ‘ , ‘a rational number ‘ , and ‘an irrational number ‘ . We know that these terms are related to the Mathematical concept called NUMBER SYSTEM . Number system is a mathematical representation of a number of a given set . We will be learning all these one by one .

Complete step-by-step answer:
Starting with the term ‘Real Number ’ – We can define any number that can be found in the real world as a real number. Or we can say that any number that we can think of, except complex numbers, is a real number. The set of real numbers, which is denoted by ‘R’ . Real numbers are the numbers which include both rational and irrational numbers. For Example= $ 1.5,2.5 $.

Rational Numbers – We can define by saying any number which can be represented in the form of p/q where q ≠ 0. Also, we can say that any fraction fits under the category of rational numbers, where the denominator and numerator are integers and the denominator is not equal to zero. It is denoted by ‘Q’. For Example= $ 1.5,2.5 $

Irrational Numbers – We can call An irrational number is a real number that cannot be expressed as a ratio of integers, The meaning of irrational is not having a ratio or no ratio can be written for that number. So That means the number which cannot be expressed other than by means of roots. It is denoted by ‘P’. For Example = $ \sqrt 5 ,\sqrt {11} $ .

Whole numbers - The whole numbers are the numbers without fractions and it is a collection of positive integers and zero that includes all the positive integers from 0 to infinity. These numbers exist in the number line. Hence, they are all real numbers . These are denoted by ‘W’ . For example \[0,{\text{ }}1,{\text{ }}2,{\text{ }}3,{\text{ }}4,{\text{ }}5,{\text{ }}6,{\text{ }}7,{\text{ }}8,{\text{ }}9, \ldots \].

Integers -We can define it as the numbers which can be positive, negative or zero, but cannot be a fraction. These numbers are used to perform various arithmetic operations , like addition, subtraction, multiplication and division. The examples of integers are, \[1,{\text{ }}2,{\text{ }}5,8, - 9,{\text{ }} - 12\], etc. The symbol of integers is “Z“.

Note: Always Remember that there are no real numbers which are neither rational nor irrational numbers .
We can say Zero is considered as both a real and an imaginary number, since 0 is also a non-positive number, therefore it fulfils the criteria of the imaginary number. On the other hand , 0 is also a rational number, which is defined in a number line and so it is a real number.
Keep in mind that the rational number can be either positive or negative.
We must know that the decimal expansion of an irrational number is neither terminating nor recurring.